Thermodynamics Formulation of Economics Burin Gumjudpai A

Economics)

2019 Burin Gumjudpai A Thesis Submitted in Partial Thesis Submitted A School of Development Economics of Development School Master of Economics (Financial (Financial of Economics Master Thermodynamics Formulation of Economics Formulation Thermodynamics Fulfillment of the Requirements for the Degree of Degree the for Requirements of the Fulfillment National Institute of Development Administration Development of Institute National

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Chairperson

Dean Major Advisor Major Committee Committee Committee

Apinunmahakul, Ph.D.)Apinunmahakul,

Burin Gumjudpai School of Development Economics of Development School ______/______/______Thermodynamics Formulation of Economics Formulation Thermodynamics

Ph.D.) Athakrit Thepmongkol, Professor (Assistant Ph.D.) Professor Yuthana Sethapramote, (Associate Professor Amornrat (Associate (Assistant Professor Pongsak Luangaram, Ph.D.) Luangaram, Pongsak Professor (Assistant

(Associate Professor Yuthana Sethapramote, Ph.D.) Professor Yuthana Sethapramote, (Associate Approved This Thesis Committee Examining Submitted The in Partial

Fulfillment of the Requirements for the Degree of Master of Economics (Financial Economics (Financial of of the Degree Master the Requirements for of Fulfillment Economics).

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disposable. disposable.

- ect ect structure ﬀ

symmetric symmetric consumers with one type of -

he he EoS. Having explicitly known EoS of the

ABSTRACT d average personal wealth possessed by consumers as Thermodynamics Formulation Economics of Thermodynamics Gumjudpai Burin Economics) Economics (Financial of Master 2019 of of thermodynamics are discovered. With deﬁnition of truly

ture ture diagrams. With the rules, EoS are classiﬁed into two We follow Carathéodory approach which requires empirical cient cient market. The commodity is ﬁxed asset and is non

ﬃ Carlo Carlo simulation for t -

consider consider a group of information side economics EoS. The price takes a role of intensive variable, demand -

economy economy and its coordinates lays reasonable assumptions of Hamiltonian and partition function which are central aspects in application of statistical mechanics to economics ﬁnance. and quantity quantity as extensive variable an temperature. The economics EoS is of the new class, the Class III. We proposed exact form of the economics EoS for econometrics analysis. At last we propose the way to perform Monte rules rules and the effect struc classes. Applying the conventional thermodynamics and the new rules, we can identify demand variables. variables. In investigating EoS of various system for constructing the economics EoS, unexpectedly new insights endogenous function, criteria rules and diagrams are proposed in identifying the status of EoS for an empirical equation. The rules and diagrams are named e commodity commodity in an e We are interested in seeing if there is some connection of thermodynamics formulation to microeconomics. existence of equation of state (EoS) and coordinates before performing maximization of Degree Year ABST RACT Title of Thesis Author

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January 2020 January Burin Gumjudpai Burin

Naresuan University for Naresuan University research and facility Associate ACKNOWLEDGEMENTS This work is supported Graduate by School of Development Economics, NIDA

Institute for Institute Fundamental Study, discussion. for Yuthana Sethapramote Professor Dr. ACKNOWLEDGEMENTS and Thailand Center of Excellence in Physics (ThEP Center). The author thanks the

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8 v 1 1 2 3 4 4 6 6 6 6 8

iv ix

iii 15 16 16 10 10 12 12 12 13

Page ......

......

an Empirical an Law

- Planck “Classical” Postulate “Classical” Laws Planck - ......

TABLE OF CONTENTS OF TABLE ......

......

Clausius - static Process of static Process Processes and Types - ......

......

Thermodynamics Potentials and Legendre Transformation Potentials and Legendre Thermodynamics and System Isolated Closed System Quasi Kelvin State of Equation Equilibrium Conditions Thermodynamics Thermodynamics Space, Extensive and Intensive Space, Coordinates Extensive Thermodynamics and Intensive Model Building Nature of Economics and of and Nature Uniﬁcation Finance and Economics Model Building Thermodynamics and in Economics on Equilibrium State Notices in ofState of Equation Thermodynamics Mathematical Insuffciency the Equation of Economics: State of Piece of Missing Speculation

2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.2.1 1.1.1 1.1.2 1.1.3 1.1.4 Demand, Supply Price Supply and Demand, Impact of the Study of the Impact the Thesis of Organization of Physics Essence Thermodynamics Background and Signiﬁcance of the Problem Signiﬁcance and Background Objectives Study of the Scope

2.3 1.5 2.1 2.2 1.2 1.3 1.4 1.1

CHAPTER 2 THEORETICAL BACKGROUNDS CHAPTER 2 THEORETICAL TABLE OF FIGURES TABLE CHAPTER 1 INTRODUCTION ABSTRACT ACKNOWLEDGEMENTS OF CONTENTS TABLE

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7 vi 38 39 42 44 27 28 28 29 30 30 30 31 32 33 34 36 37 1 18 19 21 21 23 23 24 25 25 26

......

...... ect ...... ﬀ ......

......

grability ......

ics System ......

......

Linear with Price Linear ......

......

Linear with Price Linear ......

......

d an

......

Empirical Definition of a Thermal Process Definition of a Thermal Empirical Definition of EntropyEmpirical Equilibrium Temperature and Definition of Thermal Empirical Statement of the First Strictly Law Types of System to Other Application Thermodynamics View of General Equilibrium, of Constraint Conservation View General Thermodynamics Preference and Problem Optimization Constrained in Thermodynam Optimization Constrained in Consumer System Optimization Constrained Exogenous as E Considered Constraint Changing State and Variables Inte of Existing Intensive

3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.5.1 3.5.2 3.5.3 3.5.4 3.5.5 3.5.6 First Trial on Setting the Zeroth Law of Thermodynamics Version of of of Version the Thermodynamics on Setting Zeroth Trial Law First Economics with Market Price with Demand and Unitary Market Conclusion and Chapter Critics Carathéodory Approach Carathéodory this of thesis Direction Physical Agents Agents Social and Physical Samuelson Fisher and Walras, (1949) Lisman (1999) Saslow Analogies Macroeconomics of Thermodynamics Equilibrium General and Optimization Constrained Deriving of Demand and Supply Functions Demand and of Supply Deriving Empirical versus Laws Theory

4.4 4.1 4.2 4.3 3.7 3.6 3.4 3.5 3.1 3.2 3.3 2.4 2.5 2.6 CHAPTER 5 EFFECT STRUCTURE DIAGRAM CHAPTER 5 EFFECT CHAPTER 4 EOS OF A CHAPTER 4 EOS OF MARKET: A WRONG TRIAL CHAPTER 3 LITERATURE REVIEW CHAPTER 3 LITERATURE

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65 67 69 54 54 55 56 56 57 57 58 58 59 61 62 63 63 45 45 46 47 48 48 48 50 52 53 53 54 vii

......

erential ......

...... ﬀ

......

ams ......

......

side EoS with the Basics of of sideEoS EoS Basics with the side EoS Di with Total - - ......

......

SIDE EQUATION OF EQUATION SIDE STATE - ect Structure ect , Market Does Static. Not Stop But , Market

ﬀ Side Economics Version of Mechanical Work of Side Economics Version Side Economics Version of Thermal States Thermal of Side Economics Version Equilibrium Thermal of Side Economics Version - - -

......

Side Equation ofSide Equation State ect Structure and Class EoS and Structure ect III

- Carlo Simulation of the Demand SimulationCarlo Function the Demand of ﬀ - Modeling of Demand Modeling of Distribution Function Case Probability of Discrete Case Demand As E of Types Two Equilibrium Proposing Economic Gas EoS of Real Virial of Demand Modeling Price and Temperature Are Not Analogous Temperature and Price Demand Demand Role of Variables Role of EoS Representations of Other Paramagnetics as and Hydrostatics Class Diagr and Effect Structure II Class I Endogenous and Exogenous Effects and Endogenous

6.3.3 6.4.1 6.4.2 6.2.4 6.2.5 6.2.6 6.2.7 6.3.1 6.3.2 6.2.1 6.2.2 6.2.3 5.1.2 5.3.1 5.3.2 5.1.1 Monte Conclusion Chapter Using EoS in Modeling of Demand Function for Econometrics of for EoS Function in Modeling Demand Using Rules of EoS RulesE of Demand Truly Endogenous Effect Truly EoS for Diagram Structure PropositionEffect of EoS of Proposed a 4.3 in Section Testing Conclusion and Chapter Critics Roles of Thermodynamics Coordinate Variables in an EoS Variables Coordinate Thermodynamics Roles of

6.5 6.4 6.3 6.1 6.2 5.4 5.5 5.2 5.3 5.1 CHAPTER 7 CONCLUSIONS BIBLIOGRAPHY CHAPTER 6 DEMAND

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71 viii ......

BIOGRAPHY

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2 49 51 5 58 38 39 41 41

.. Page ...... s the

......

Competitive

- ......

(b) (b) Linear ......

and and

......

...... versus versus

......

...... FIGURES

...... Dimensional Surface (b) Surface (equation Surface (equation Dimensional(b) Surface

- ......

TABLE OF OF TABLE ......

......

Makes a Wrong Diagram. This is Because, in Say’s Law, the Supply Affects Supply the Affects in Law, This Diagram. isSay’s a Wrong Because, Makes

Figure 6.1: Effect Structure Diagram of a Group Structureof of a 6.1: Effect Diagram Consumers in Perfect Figure EoS). (Class Type Market III Unitary Price Demand and Supply as Linear Function of Price. On the Right i On the Price. of Function Priceas Demand andLinear Supply Unitary with Coordinates Represented the Extensive and Diagram Intensive Arrow by Allowing an the Diagram to to Apply Say’s from 5.3: Trying Law Figure not Exogenously, Endogenously. Demand Figure 4.4: (a) Isothermal Curve (b) Isoprice Curve 4.4: (a) (b) Isoprice Curve Isothermal Figure in Endogenous EoS of Truly Variables 5.1:Diagram Showing Effect Figure (Lower). (Upper) Paramagnetics System and System Hydrostatics with Market of the Diagram Endogenous EoS 5.2: Truly of a Proposed Figure Effect Figure 4.2 : (a) Unitary Price Demand:Hyperbolic Curve 4.2 : (a) Unitary Figure Curve Supply Price as Two Gas 4.3: (a)a of EoS Ideal Figure Demand Price Elastics of with Unitary Possible a EoS of Market (4.18)), Curve Price Supply Curve (b) 4.1 : (a) Price Demand Linear Linear Figure

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and and

framework of called the model. - to the subjects. This

their mentality was not much mentality their

(Chatterjee, 2016; (Chatterjee, Eichner, 1983;

(Comte, (Comte, 1856; Quetelet, 1869)

Chatterjee, Chatterjee, 2016; Jovanovic & Schinckus, ( CHAPTER 1 CHAPTER INTRODUCTION nomics were still were nomics young, s in economics and ﬁnance. This is due to disruptive

. teria. teria. the In past, economics and failed finance to passed cient conditions in the aspects that their theories could not be ffi trained people took some major parts in developing - tances. tances. Moreover science must be deducted from postulates awaiting Key Key features of science emphasizes on predictability power of empirical When sociology and and eco When sociology Background and Significance of the Problem Similarities of mathematical relations in economics and in physics have been . erent erent from physical sciences. Social sciences were coined social physics as their

monetary monetary economics) and Jan Tinbergen (dynamics model of economics analysis). Ever since, social sciences and economics have been developing tools and concepts is just as similar to how reasoning in physics does the role in its development. Tools and ideas were brought from old classical physics in developing social physics and some physics economics in the early 20th century. For example, Irving Fisher (utility theory and diff postulates and theories were necessarily laid out both deduction and induction (inference) reasoning were framed validation validation from empirical fact development of digital technology and data sciences 1898) 2009; Veblen, Schabas, Considering Considering epistemological approach, validation of what could be comprises science of some cri considered as epistemological su The empirically. have recentvalidated decades seen much improvement on theoretical 2017) models to real phenomena. Repeatability of the prediction must hold under the same circums confirmation coming from empirical facts or empirical laws, so noticed noticed as well as mathematical analogies of the equation of motion of fluid dynamics to financial derivative pricing equation 1.1

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2 re re

ters of ects ects that ﬀ culty might culty ﬃ

hence variables ea. ea. Although there is no yet These approaches consider aaquie, aaquie, 2007; Mantegna & . (B ols of thoughts that can not be

ling. ling. Apart from these subﬁelds, quantum ﬁeld theory, path integrations,

based mode - that, human’s memory (historical) e

conomics due to complexities of the subject. The subject. di of the conomics to complexities due nomics, ﬁnance and social systems andom andom walks or agent Model Building Nature of Economics and Finance and and Uniﬁcation Finance of BuildingModel Economics Nature

Unification Unification of economics concepts and ideas into one single theory might not 1.1.1 Economics and finance are social science subjects with strong charac many many other subjects of applied mathematics and physics such as fluid dynamics, unification unification of theories into one single framework is key id system system such as particles, atoms or molecules. As economics a and social result, sciences concepts are divided and into scho ideas in firmly practical empirical laws albeit the first principles (key assumptions) are well established, yet awaiting to be examined. On the other hand, in natural science, be be diversity or heterogeneities of human choices. The complication of choice might also come from technology development that makes human forms preference more and more complicated. Apart from make microscopic agents of social system (human) much distinct from physical finance could be serious scientific subjects such as physics or or be serious subjects as could such chemistry. physics finance scientific aim of e important be model building. Both are also based on some postulates or assumptions empirically which backedup are with data and facts. Amongst social sciences, economics and finance inherit nature of scientific disciplines the most, due to their quantitative natu of study and their assumptions made as their first principles. Hence economics and researchers to explored. researchers Stanley, Stanley, 1999; Richmond, Mimkes, & Hutzler, 2013) either individual agents either at microscopic scale or at each time scale in economy. Only classical thermodynamics views the problem aggregately and are evaluated at average. Gaps of these interdisciplinary knowledge are awaiting for complex networks, quantum mechanics, classical dynamics and classical thermodynamics that are under serious exploration in applying to eco on their own rights. In finding resource allocation and price formation, develop its own concept up while physical economics approaches are to use statistical mechanics or physics of r there

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ect. ect. ff iced iced by Unification Unification of

. thermodynamics) thermodynamics)

between between social and physical ized and larger in coverage of the in the same spirits as physics, may

known as equilibrium - (Fisher, (Fisher, 1892; Samuelson, 1960, 1990)

(Lux & Westerhoff, 2009)

conomics

mework of thermodynamical economics is found, all

Notices on Equilibrium State in Economics and Thermodynamics on in Equilibrium Economics State Notices

It It is learnt that financial crises in the past decades can not be predicted in 1.1.2 We notice that both thermostatics (well rizons and new perspectives of economics and financial concepts. This might ised long ago by Fisher and Samuelson beneficial to its rich applications in economics and therefore to and therefore infinance. economics to its rich applications beneficial improve improve the way we model economic system and phenomena. the Yet to way come, we further part explain of economic thermodynamics includes theory of phase transitions, if the true fra techniques and theoretical frameworks of phase transitions would be as well much ra albeit not turning to be Analogous theoretical frameworks neither of economics to thermodynamics would open new a popular nor mainstream ho research discipline. learners. learners. Speculation that the two subjects have some similarities in their structures is not an insignificant issue. Historically, connections thermodynamics had between been the abandoned and economics a and formal links of the two subjects was and and economics are theories relying on existence of equilibrium states. Some variables of the two theories can be Moreover, thought similarities in mathematical of formulations of the both subjects are cause not (or influence) and the e systems systems as a first step. Along the way in future, we hope to follow track of physical unification. theories better better economics theory, it should be more general economical phenomena. It is far hoped that the unified framework is able to explain the larger economics and financial phenomena eventually. In the quest of unification of such theories, we shall begin with making analogies theoretical theoretical frameworks in economics and finance, help leading direction of modifying theories and ideas in economics and finance, with even unnecessary of amending first principles of economics and finance. If there is a final final unified theory of nature, nevertheless significant progress past in the been made decades. few have and advancements frameworks of contemporary e

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) ) ) )

is a 1 2 3 4 . . . .

1 1 1 1

( ( ( (

(

(state (state variables in ) Thermodynamics

ck ck all other relation (

afterwards the pressure

erential

ﬀ does does not give a complete physical exact exact di

ally, ally, however they are lacks of some

. The regressed equations are also constructed variables in economics) and of which variables

ciency of Equation of State in of State Equationciency of stock re, volume, temperature and molar number of the of volume, and gas number molar re, temperature the EoS

r the temperature can not directly make any changes in volume

), are pressu are

ling economics phenomena with econometrics, ﬁrst consideration is to

Speculation of Missing Piece of the Equation Economics: State Piece of Speculation Missing of Mathematical Insuff Mathematical

a a good assumption or suitable economics theory. Therefore we can consider is the gas constant. Before this we have learnt speciﬁc cases of this law. These of have learnt this These this law. cases we constant. speciﬁc is the gas Before In In mode 1.1.4 1.1.3 In elementary thermal physics, students are taught of the ideal gas law which is

ects ects the change in volume. This gives a significant clue that the mathematics of the ff thermodynamics thermodynamics or known as some variables as independent performing regression variables analysis on and data. This dependent is performed without variables equation the of concept state, and of hereafte hence without considering of which variables have pick up equation equation of state of an ideal gas realization. It brings about our curiosity to investigate and che of equation these types in Thermodynamics. variables and state other all of between physical physical sense. For example, look proportional constant at Charles’ law, but instead the temperature makes change in pressure first and a and Charles’ law Charles’ and Each keeping all other conditions or variables constant. All these laws are relations of two variables. They are correct mathematic Amontons’law whereas, and such Boyle’s law as are actually the equation of state of an ideal gas. The law ideal state gas. The states of of an the equation actually

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)

t in ﬂow 5 . 1 ( erent erent contexts of ff ed ed in the manifold. endent endent of path in the

ion of variable with inexact

erential erential are not clearly made

ﬀ

) and temperature (as a background

s in the subject are not necessary

erentiality erentiality is indep variables are to be extensive or intensive, deﬁned deﬁned with the coordinates, for instance,

, where , where +

erent erent sets of measurements and hope to have

her her types of manifold in di If If there is such an EoS analogous concep

ﬀ

. analogous analogous space of economics must be found

In In this manifold, all elements have roles of

* .

)

) . All other variables are not includ

(energy (energy transfer in Thermodynamics or known as

(

), intensive coordinate (

Colell, 1989)

( -

of of variable with exact diff (

erential

thermodynamics thermodynamics potentials n economics is real intrigue to see in future. In the far future, we hope to In In economics, there is also manifold of the theory conﬁrmed existence of the In In thermodynamics, there is a space of the theory. The coordinates of the function function of commodities or ot inexact inexact diff

erentiality depends onerentiality path. application application i have a new direction of relating di theory. some extension economics to standard (Debreu, (Debreu, 1959; Mas economics, a thermodynamically together with the EoS which is indeed the equilibrium surface of the theory. Potential is to be found and the hope to see a complete analogous theory with fruitful stated stated above, are not considered. The coordinates or to be potentials, distinction or of which of which variables are or to of which be variables are to be exact or inexact di diff value mathematical analysis. However, the EoS aspects of the manifold’s element members, Within the elements of the manifold, there is a mathematical relation relating these coordinate variables. We are talking about the EoS. Having a space of the theory as stated, integration coordinate space of the theory. On the other hand, integrat Note Note that in general some extensive coordinates but variable internal energy thermodynamics coordinates extensive coordinate axiom) founding manifold, emerging from in the quantity have have in economics). variables space of theory form a set of manifold. Element of this set must be categorized as

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6 Carlo -

ling

In In chapter 5, there is equation equation of state in .

existing works on the area in

udpai, udpai, 2018) ect structure diagram in the EoS with ﬀ

(Gumj

rspectives in econometrics mode rspectives considered at clearing condition. clearing at considered n thermodynamics n thermodynamics formulation of economics

cient and is and cient

introduce introduce equation of state for econometrics modeling and Monte

Taking Taking the equation of state and natural thermodynamics space coordinates o investigation New pe Possible founding new Homogeneity of consumers, producers and of and commodities consumers, producers Homogeneity Information spreads symmetrically and instantaneously throughout the is eff Market equilibrium. at considered are All variables To improve mathematical expression of the To identify coordinates of the space for the equation of state economics system equation of of an state To formulate of the To

Organization of the Thesis of thesis is plannedout necessary andThe understanding to lay thermodynamics Impact of Studythe Scope of the Study Objectives 5) 1) 2) 1) 2) 3) 4) 1) 2) 3) 4)

improvement improvement in mathematical expression of the equation of state in Thermodynamics and the author proposes new founding of e economics economics in chapter 2. We discuss previous and chapter 3. The trial on constructing the EoS reported is by reported in the chapter author 4 in which Gumjudpai was 1.5 1.4 as a founding initial basis prior to deducing to other initial basis prior to deducing aspects a founding as market. simulation 1.3 thermodynamics formulation economics of thermodynamics 1.2 physical deeper insights that such reﬂect it can thermodynamics

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7 logy logy and for and and Gumjudpai and

scussed. scussed. We suggest EoS menological formulae or and and 6 are reported in Gumjudpai

. We conclude our thesis in chapter 7. chapter in thesis our conclude We . hapramote, 2019)

(Gumjudpai & Sett

(Gumjudpai & Sethapramote, 2019) Sethapramote, & (Gumjudpai

ling ling of demand function for further econometrics methodo Carlo Carlo simulation. Some results in chapter 5 -

Monte and Setthapramote Setthapramote criteria criteria rules for an EoS status relations. The ﬁnding in chapter 5 helps disproving the of EoS proposed in chapter 4. In empirical or pheno chapter 6, the EoS of group of consumers is proposed and di in mode

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. - e, e,

) )

2 1 . . 2 2 ( ( ) over tim

(EoM) (EoM) which

motion

of as as the result of kinetic

e e those derived from Hamilton’s equation equilibrium state. -

of -

erent from the rest of physics. In

ﬀ known EoM of classical dynamics is the

∫

Lagrange Lagrange equation or Hamilton’s equations which ∑ CHAPTER 2 CHAPTER -

thermodynamics thermodynamics (correct name should be thermostatics) electrodynamics, electrodynamics, quantum mechanics, quantum ﬁeld theory,

which which includes physics derived from Hamilton’s principle such

dynamics dynamics is named modern thermodynamics. Modern THEORETICAL BACKGROUNDS THEORETICAL : Key concept for mechanics is the Mechanics Equilibrium

Essence of Physics There are two branches of physics, the ﬁrst ar Mechanics 1) 2)

or spacetime (in theory) is the action (in ﬁeld spacetime or quilibrium thermodynamics is regarded as classical thermodynamics while non

energy energy subtracted by potential energy. Well law second of motion,Newtons which is varied to obtain the Euler are the EoM of the theories. Lagrangian function deﬁned can can be derived from Hamilton’s principle. Paradigms of thermodynamics is without the Hamilton’s principle hence is mechanics, integrations very of a postulated scalar quantity (the Lagrangian, di E equilibrium thermo is the attempt the out tothermodynamics include as as classical dynamics, so forthand and relativity general (least (least action) principle these two branches as shall dub here We thermostatics). and the second is equilibrium thermodynamics (or 2.1

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) ) 9 ), ), ).

) ̇

2 (

( e), dimensional dimensional (generalized ) but we can - is volume (

)

) axes. Existing of

(

er er to calculate physical

ded in some physical or mbedded in 3 (Euclidean (Euclidean spac

) or ( ) process process (isentropic or adiabatic) , of thermodynamics space. The

eld

ﬁ

(EoS). The EoS is constructed not

given given set of coordinate values are

- ( ) and thermal extensive coordinate is

), ( which which is the EoS. Hence existence of the

dimensional space ( ly. Chemists and engineers contributed state )

), ( (

), mechanical extensive coordinate

equation

(

dimensional dimensional constraint surface e - subjects are such as : Thermodynamics was formed with empirical formulae that

momentum, time).

is in form of is in form

relation between (

is ﬁxed canonical

as as a function of coordinates, that is a

is a there

1) 2) Thermodynamics it reads whereas Therefore Therefore the EoS is a 2 thermodynamics space. The space enables one to define a thermodynamics potential function surface, constraint EoS hence reduces 2 degrees of freedom out of the 4 degrees of freedom, resulting in a 2dimensional geometrical object described by a space of 3 coordinates ( view view only 3 dimensions as ( infinite equilibrium states connected by an constant equivalently results in equilibrium surface EoS results in two constraints: is the minus sign of pressure thermal intensive coordinate is temperature ( entropy (S). Thermodynamics space is a 4 physicists physicists in the early 20th century. These (plugged into) empirical four postulate laws formulae of thermodynamics must in ord be used in quantities such as internal Considering simplest closed energy hydrostatics system, mechanical intensive coordinate ( and energy transfer (i.e. heat and work). serves serves as models of how substance behaves in relation with heat These and models temperature. are known as theoretically like the EoM but empirical greatly to the earlier developments of the subject before it was wrapped up by (generalized (generalized coordinate, generalized coordinate, velocity, time) or Laws Laws of physics are indeed a constraint abstract surface spaces. embed All the EoM with geometrically a constraint surface embedded in a space of the infinitelytheory. The coordinates space of mechanical

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)

10 )

4 . 2 and and

( extensive

boundary) boundary) ), internal

law), internal

): th thermodynamics

, (

with

(in the 0

), electrical polarization ( polarization electrical ),

is of the same spirit of the deﬁnition space

) is a combination of

To see the frameworks, we need to

). Examples of intensive quantities are

) mechanical

(

dependency dependency and origin of variable, we can law).

the intensive quantities are in opposite, that is

), magnetization ( magnetization ), nd

thermodynamics

from

(

. Extensive quantities depend on size . Extensive depend quantities (i.e . and entropy ( mentioned statement is not much useful here in - nd other speciﬁc quantities of the extensive quantities, (in the 2 (in the )

. Heat term

) a (

coordinate

pair quantities

), heat law) and law)

st extensive ( volume are Examples (Buchdahl, 2009)

intensive

Thermodynamics Space, Extensive and Intensive Coordinates Space, and Extensive Intensive Thermodynamics mechanical . Considering aspects of size 1) ), temperature (

independent. independent. Examples of extensive quantities are volume ( and and ), work (

(in the 1 (in the

In In thermodynamics we have

dynamics dynamics coordinate space. Hence to obtain the EoS and to identify the rize thermodynamics coordinates into sixrize thermodynamics coordinates types. 2.2.1 Quantities in thermodynamics can be viewed quantitatively as Thermodynamics All thermodynamics quantities are all derived from EoS embedded in

coordinates catego number number or mass. The above picturizing the frameworks of thermodynamics. space. of variables coordinates thermodynamics these as consider energy energy ( pressure ( i.e. any extensive quantities can be made intensive by dividing them with molar quantities of the system of consideration whereas it is size thermodynamics thermodynamics postulates that result in what quantities and state to exist and how related are they thermo thermodynamics coordinates are the most important. Let us see the consequence of energy energy 2.2 for hydrostatics system. Work term, dubbed the mechanical pair. Postulates of thermodynamics deﬁne

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)

11 eir eir

ential.

er where where we ﬀ

) as (

erential ) forms heat term, , ( ):

diff

dependent dependent hence th

), magnetic ﬁeld ), magnetic ﬁeld -

of of some form of energy.

) or ( ) or ( exact

denotes denotes di inexact

ow deﬁnition , ( ﬂ

are are path cribing cribing with (

. Examples are such as

pair particles

of mechanical

an an entity as of system.of ) and - - thermodynamics thermodynamics deﬁnition are mostly of

): ),

from

ive coordinate from classical thermodynamics fromive classical thermodynamics coordinate

Chemical Chemical potential is viewed as a ﬂow potential , ( . number

erentials erentials are said to be mechanical ): ﬀ or

from from non (paramagnetic (paramagnetic work). The pair (

), work ( , ( erential erential of a function. On the other hand, transfer energy erential where the symbol where erential the symbol ): ﬀ

potential

) forms a term describing energy that transferred with that transferred ) mass, forms a energy term describing called called

coordinate ( -

of of system

so number

of of an open system. A system des hemical ) is - molar number are for a or extensive coordinate number Molar of particles C with mass system for a coordinate is potential intensive Chemical entropy thermodynamics classical is extensive from coordinate Entropy temperature is intens Temperature intensive value pressure (negative of) Examples are

for for exact di

), electric ﬁeld intensity ( ﬁeld intensity ), electric

5) 6) 3) 4) 2) . The pair (

the second law. the second law. the zeroth - -

which which is a form of energy transfer These These thermodynamics coordinates are continuous function such that they are A pair of coordinates

into or out independent independent hence their di

erentials are are diffinexact erentials

ﬀ

use symbol (of ﬂow) term, i.e. heat ( di as hydrostatic mentioned before. is knownsystem coordinate as path The pair ( (mechanical work) or which is a thermodynamics coordinate, not thermodynamics potential not thermodynamics is a coordinate, which thermodynamics mechanical or electromagnetic origins. Product of the pair forms work term, system with mass exchanging into and out into with mass exchanging and system exchanging into and out postulate postulate intensity ( intensity

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

is is

12 ) )

5 6 . . 2 2 ( ( ) system

independent ), - transformation

because they are

adiabatic

) is total useful work (or (or

Legendre function ), Helmholtz free energy,

) which is a sum of kinetic isolated state

). It is deﬁned with the Legendre the system has been through some

). One potential can be transformed

Gibbs potential, (

of system. a System

nal energy ( d by useless thermal energy ( energy uselessd by thermal

implication. This transformation is Legendre

exergy

coordinates. coordinates. The status of thermodynamics potentials is

) and grand potential, ( is the system forbidden any exchange of mass between the

static Process and Process Types ofstatic Processes -

system erential erential are exact. They are regarded as

and it is known as the it is knownand as ﬀ Quasi Closed System and Isolated Closed System Thermodynamics and Transformation Potentials Legendre Thermodynamics

allow allow any exchange in mass or energy transfer between its internal and is the useful energy of the system.

closed

can can be transformed to energy, it contributes also to useful energy. Hence 2.2.4 A system in equilibrium when evolving, it goes out of equilibrium. Its 2.2.3 A 2.2.2 Thermodynamics potentials are not the coordinates. They are path

formation. formation. The Helmholtz free energy is derived from the energy that keep the system in its shape or in that keep its shape its structure, the system the energy

s ), Gibbs potential, (

process. process. coordinates changes to new values. It is said that system system and environment. might allow form It of transferenergy as heat ﬂow and work receiving to the system or given from the system. An does not regions. external

plus If than larger of of total internal energy with dual coordinates ( subtracte as internal tranformation energy hence energy energy at all degrees of freedom of the system, enthalpy ( ( to new potential with new physical tran similar to gravitational or electric potential ﬁeld in mechanics or electromagnetism such that both of them are thermodynamics function potentials are deﬁned the in inter coordinate space. Examples of hence hence their di function of thermodynamics

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

. 13 , it is

. Given they they are isobaric is called

. The internal internal . The , it is called

, in the system. system. It is , in the

value value scalar function that can be deﬁned deﬁned or known, i.e - - . For constant

. The process with constant isentropic . the In process without heat ﬂow, thermodynamics thermodynamics taught in universities follows the process

Planck “Classical” Postulate Laws Postulate “Classical” Planck - isovolumic static , it is called -

Clausius quasi - . These terminologies will be to later in thisreferred thesis.. These terminologies

The First Law The First energy, law of internal existence The gives ﬁrst The Zeroth Law The Zeroth bodies. The equilibrium between zeroth law thermal The deﬁnes time dependent dependent space , it is called

Kelvin

2) 1) 1) 2)

e e a postulated quantity by the zeroth law, at thermal equilibrium . For constant adiabatic equilibrium condition, value of coordinates cannot be measured or realized

2.2.5 Traditionally, postulates of gy is sum of kinetic energy at all degrees of freedom, of freedom, at is sum degrees all of kinetic energy gy h between the two states such that the curve of process can be realized. This type ndeterministic. ndeterministic. In order to have some process, we have to inﬁnitesimally changes the

ener as expressed ordinal ordinal ranked from low to high. This scalar temperatur is hence the temperature, temperature must be time independent (steady state) and the same everywhere in the system (homogeneity). thermal thermal equilibrium condition is that there is Thermal equilibrium no implies heat that there exchange is a between single bodies. foundation foundation laid and brought together that state classical version known as postulates by Kelvin, Clausius and Planck. These For For constant known as coordinate coordinate value at new state can be measured. We can interpolate the equilibrium pat of process is the isothermal and and most cases, the dependencies are i not well coordinates to new values and wait until it soon comes back to equilibrium state. The In In out of they are because

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

14 ) ) ) ) ) )

tells tells

9 7 8

. . . quasi 12 10 11

2 . . . 2 2 d 2 2 2 ( ( (

( ( (

of of the system. - scalar scalar factor a as

dependent quantity, dependent

)

). For a system with n moles

to the changes in mechanical

which is deﬁned as as is deﬁned which

erential. erential. The last term,

)

w mechanics has a channel to link

mole mole carries into or out

(

∑ ( )) that deﬁne path that deﬁne ))

)

(

is established as extensive potential, for . The law tells that total entropy of the system and

where where δ denotes inexact diff

decreases, i.e. decreases,

). Once The Third Law to process approach it steps of that states inﬁnite third law The needs of Consequences LawsOther Thermodynamics of heat law term introduces The ﬁrst The Second Law of describing quantity degree postulated introduces This law new

such as the hydrostatics term, the hydrostatics work as such

4) 5) 3)

and and heat, the entropy,

is a potential function or ﬁeld deﬁned on the thermodynamics coordinate

(

) (such as pressure and volume and pressure ( ) (such as

is the chemical potential. Moreover, this is ho

isorder

multiplication factor of the system, it follows that the system, of multiplication factor of substance, consequence of these three laws three laws gives of these substance, consequence of that, Hence space of consequence of the zeroth and the second law, zeroth of the the second and consequence This introduces thermodynamics space coordinates ( absolute zero temperature at which it is postulated to be zero entropy state. which it is entropy to be zero postulated at temperature zero absolute and and for a closed system, entropy is maximized at thermodynamics equilibrium. The equality is the case of reversible process that keeps all steps statics. of the process D never environment with thermodynamics. The law introduces thermodynamics ( space coordinates of The The ﬁrst law also introduces the connection between work, how much energy that amount of substance

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

, ) a ) ) ). ).

15 )

) ) -

). If 15 16

. .

. 13 14 2 2

. .

) 2 ( (

2 2

(

( (

re re (

he he process of

(

thermodynamics

, that exists in t

(ideal gas law) (ideal gas (Curie’s law) (Curie’s

∑

, the coordinate space a

)

anical pairs in one system. The system is

naturally comes with a constraint relation

) , ) can be directly derived, be can

(

Empirical Law Empirical

The The EoS is hence deﬁned at

( (

equation

cts cts relate these coordinates together in the EoS

when combining, when

)

16 . 2 Euler’s ( ) is deﬁned with these coordinates. There might be a composite

and and

)

The hydrostatic case, it case, reads hydrostatic The and the and Equation of State EquationState of Form Form of the relation is found empirically. In classical thermodynamics, 15 . .

is the Curie constant. 2 (

2.2.6 The postulates stated above do not relate the coordinates ( known as a composite type however equation the constraints are separable as example, and and heat term. Empirical fa constrained surface embedded in the potential space. (such as With this setting, thermodynamics physical system as such there are two mech equilibrium the system must be identiﬁed mechanical with and thermal coordinates must boundary be found such that of they describe the work inner and outer regions. The substance, paramagnetic of and where obtained obtained from observational or experimental facts. This is the EoS, or in a closed hydrostatic system, constant entropy (isentropic), that relates the three the EoS of ideal an gas, examples are coordinates together. Familiar together. together. In a closed hydrostatic system, the coordinate space there is are such a set of ( states with ﬁxed value of However to have such a set of constant

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

, -

16 ) )

18 19 . . 2 2 ll known ( ( equilibrium

system it system and

, market is self

mechanical or mechanical

is maximum whereas all usion or exchange of usion or exchange

) mechanism mechanism is we ﬀ

- economics

of thermodynamics

( school

) take the same value throughout the the value throughout the same ) take

but we need to keep to in mind it that is need made but we

)

are minimized. are

)

classical or or erent parts parts erent the system. of

ﬀ

)

(

)

(

variables (such as (such as variables

Temperature takes the same the takes throughout whole value Temperature equilibrium: Mechanical equilibrium: Chemical Thermal equilibrium: Thermal ( variable takes the same value throughout the whole system and it and must whole the takes throughout the same system value variable

Thermodynamics Equilibrium Conditions Thermodynamics

2) 3) 1)

Demand, Supply and Price Following Adam Smith and the 2.2.7 As consequence of these postulates, to acquire Since Since thermodynamics equilibrium is kept along the process without any

regulating regulating system and advocation of freely competition (Laissez Faire) supported so that can be achieved wealth the most. The self should be 2.3 It It is important to note that at thermodynamics equilibrium, potentials, thermodynamics entropy Aproduction. Equilibriumentropy region between and condition systemregion a B of in of the below term equation, the balance each is hence be time independent. At chemical equilibrium, there is no di equilibrium, At there timechemical independent. be di componentschemical between any whole system and it must be time independent. The system has The no system it must time system and independent. be whole of motion. types other three physical conditions must be obeyed at the same time. These are same the at These time. physical mustconditions obeyed be three no thermal at thermalhas equilibrium. process system must time The independent. be

This is realized as as This is realized from two independent EoS. Hence in composite physical system, there could be ﬁnite EoS, of independent number

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

y of of

17 ) ) ) )

) and 21 20 . 22 23

. . . 2 2 2 2 (

( ( ( ) and income

, (

. ) )

, . ⁄ ⁄

other other related good (

)

(

). The demand quantity function ﬁned ﬁned at market equilibrium with )

(

, is de

Colell, 1989) ), price of

introduces introduces a few assumptions to enlarge the

(

( of of consumption for the demand side and

and

and Hence Hence this is not the case of Robinson Crusoe

. of of a good

), price of the other related good

and Supply Functions economics Colell, Whinston, & Green, 1995; Pindyck & Rubinfeld,

)

preferences )

(Debreu, 1959; Mas (Debreu,

school ⁄ percentage in price, change ⁄

(

producers (sellers). That is for a market with some particular properties

(

In In economy, price,

price price elasticities of demand and supply are the percentage change in quantity Deriving of Demand Neoclassical , - (Luenberger, (Luenberger, 1995; Mas

)

economy which assumes one consumer, one producer and two one and producer goods. assumes consumer, which one economy scope scope of the classical school. The neoclassical school hypothesizes that individuals are rational and have production for the supply side this thesis. 2.4 It It is clear that the price elasticities are not constant but functions of price and quantit goods, of There are other types of elasticities but are not required in the context of discussion in Both Both elasticities are characters of the goods and market in the (buyers) and view of consumers or characters of buyers and sellers, there are some particular function of the elasticity. Point to one with respect Supply quantity is function of price ( level ( technology could could be function of price ( ( 2013) as as the invisible hand. The classical school brought the theory of value to the concept equilibrium price at of equality of demand and supply quantities, (

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

18 ) )

and and

25 24 . . 2 2 ( ( erent erent curves of of resources.

ﬀ

price formation scarcity

)

realistic model of economy. realistic model of -

( to -

world observations or experiments.

- )

ion,

)

discovered. discovered. This mechanism should hold in

( ( made made independently by taste or needs of each

and maximization of the proﬁt, of maximizationand

)

n under budget constraint line, using indi

(

lained lained by physical theory. For example, the ideal gas law is are are key ideas of the neoclassical school. Consumers’ behavior can

] of the buyers therefore explains of consumer behavior. From top

pirical pirical laws do not tell us why or how such things happen or can not buying commodities, consumers want to obtain maximum utility. The is revenue. Both optimizations employ the Lagrange multiplier method. On so that the price equilibrium is

allocation

Preference Preference associates with values. The preference is assumed to come with

Empirical Empirical laws are constructed from real Theory versus Empirical Laws

empirical empirical law and is exp explained with the kinetic theory of gases derived from classical dynamics. In about about fundamental issues. Empirical laws can predict and forbid events or phenomena to happen. Em happen. Theories, unlike empirical laws, are to explain facts or explain empirical laws that how or why things happen or can not happen. In thermodynamics, EoS is 2.5 Albeit under some simpliﬁed assumption, empirical laws is about facts rather than where where the empirical side, demand close which a method building econometrical helps and supply functions can be constructed from which which represent ordinal level of utility. The of production, cost minimizing supply function is derived with the aspect. aspect. In condition max[ down theoretical method, the demand function is maximization of utility functio deducted or derived from the be described with maximization of utility funct with maximization described utility be of Each consumer has his or her own satisfaction or needs of commodities so that the preference exists and the choices are made. Hence utility function is an individual allocated describing behaviors of both consumers and producers. Hence resource information information symmetry and choices are individual. Assumption of preferences and choices arises due to Neoclassical theory seeks for mechanism of understanding how scarce resources are

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

Social Social agent: (Burin) with

laws. Social Social agent: (Burin) status: (1) ics which is to with be explained

: Complexities in modelling social system

uiring of maximization of utility. Law of parking slot but parking he might choose not to use it.

man named Burin eﬁned eﬁned boundary.

ttracts ttracts positive charges, i.e. it obeys Coulomb’s law and d -

ion. Other properties follow different

Choices or Choices Options systems in physical to choose rights) no optionsbut optionsare (or There Properties Properties (in physics) or (2) spin negative charge, (1) (electron) are three properties agent: Physical Status Elasticities (in social sciences) Duties charge other property, it(electron) with negative repulses agent: Physical Names electron agent: particle named a Physical a agent: Social . Teacher has . rights to Teacher use staff

in social system, evoking game theory to take part in social sciences (e.g. in System System is what we consider and must possess some properties. A system does Physical Agents and Social Agents 4) 2) 3) 1)

er (with teaching duty elasticity) (2) father (with father duty elasticity) (3) (2) (with citizenfather er elasticity) elasticity) (with father teaching duty duty

economics). economics). For example, electron must behave as dictated by law physical and it has no rights his teaching duty elasticity, he must teach three hours a day day so on. and three hours a he duty elasticity, musthis teaching teach exists negative negative charges and a equation of mot and and (3) mass. Properties are mathematical variables. teach taxes) paying ... e.g. elasticity, voting, citizen(with duty not need to have well have its root in aspects of social agents. These are aspects to consider when modelling oragents or physical for social systems laws 2.6 empirical empirical law in the of style the EoS in thermodynam theories in traditional economics or in economics. the new thermodynamics formulation of economics, economics, laws of demand and supply are empirical. Law of demand is explained with the consumer behavior theory req supply is explained with production theory which requires maximization of This profit. is sense of serious scientific spirit in economics. We hope to find economics

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

of 20

risk

. For example, it is possible that teacher does not teach as duties

doing

in negligible. negligible. For quantum mechanics, uncertainty is associated within the Uncertainties or Systematic Risks or Uncertainties Systematic For classical physics, system is deterministic and uncertainties (or physical

The The forth aspect, option and risk created from option making, is hence main 5) n by a rule relating his teaching duty elasticity. Financial risk of defaulting in reasons why social systems is much more complicated than physical systems. than social why complicated systems is more much reasons equation equation of motions. Systematic risk is also important concept in subject of ﬁnance, e.g. in portfolio theory as systematic risk is unavoidable by optimization of ﬁnancial portfolio. risks) are Since Since social agents have options to do or not to do, defaulting hence they can create give also has debts paying its option making. root from

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

ﬁnancial ﬁnancial - approach to , determines

The balance of price, The .

(Walras, 1909)

CHAPTER 3 CHAPTER ﬁnancial ﬁnancial mathematics (or fashionably leaded, leaded, this work is not about directly taking human -

rather than thermodynamics economics of thermodynamics formulation rather than LITERATURE REVIEW LITERATURE . Price is similar to pressure that price is represent of level of ond & Winnett, 2009; Jenkins, 2005; Roegen, 1971; Tishin & It It is not our scope of study to consider statistical behavior of

). interaction interaction and consider dual quantities that represent state of the

econophysics) or - L. Walras proposed the Walras of utility proposed concept L. We shall from now discuss previous works of thermodynamical

Walras, Fisher and Samuelson Thermodynamics and economics share similarities in that they consider

rmodynamics of economy rmodynamics Chen, Chen, 2005; Hamm thought as potential energy in classical mechanics. energy as potential thought which is gradient of utility function with respect to equilibrium. This is similar concept as in quantity classical mechanics. The balance of force as of good gradient of potential energy with respect to position coordinates. Hence utility is other other represent inﬂuence (or force) (intensive that coordinate) the subsystems interact to pressure and intensive. to are trade. Both price willingness each other subsystem subsystem in system. One variable represents content of the system (extensive coordinate) and the engineering). engineering). doing such,In it the replaces concept of and utility all those follow from which. 3.1 ( Baklitskaya, 2008 economy agents in pricing of commodities as in contemporary ﬁnancial physics (or fashionably economics economics here. Not to be miss economics activities as mechanical or thermal processes and later evaluating these activities in thermodynamics the terms. This direction of viewing are indeed

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

- in 22

such as

- t as internal energy, one one to overlook or deny the en classical thermodynamics and e e past century, connection between

: is though Why Why should there be laws like the ﬁrst or

ction ction with the idea of economics

The connection initiated by Walras and Fisher the gradient is with respect to thermodynamics .

ynamics, ynamics, position coordinates in classical mechanics are (Samuelson, 1960) (Samuelson,

erentiation erentiation in ion to potential energy or internal energy might be wrong but

(Debreu, (Debreu, 1959) ﬀ .

ematical analogy betwe ” . in the economic realm.

- (Fisher, 1892)

classical classical mechanics conne - Thermodynamics Thermodynamics connection to economics turn to be of much less interest Looking Looking at thermod erent disciplines erent ff mathematical mathematical isomorphism that does exist between minimum systems that arise in di entropy entropy or energy second laws of thermodynamics holding in the economic realm? Why should ’utility’ be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead any “The formal math mathematic economic systems has now been explored. This does not commonly met attempt warrant to find more exact analogies of physical the magnitudes combinations combinations or other ways of matching variables variables in in neoclassical thermodynamics to economics. those economics In and thermodynamics formulation had th always been suspected to exist. As critique P. A. Samuelson’s were were gradually forgotten. Moreover, mismatching of potential energy minimization and utility maximization further disfavored connection trial. although utility connect From this situation, it does not imply that the connection is not possible. There are also other thermodynamics while the economics community witnessed profound application analysis to of economics mathematical thermodynamics thermodynamics connection. Fisher kept the Walrasian idea of utility gradient and its equilibrium, but the di coordinates. In this setting, utility, analogous to thermodynamics coordinates as J. Willard Gibbs (physicist) is a prime advocator. A student of Gibbs, I. Fisher hence economics propose to substitute the idea of

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

r is is is is to

) and and

urplus urplus 3 erence erence

(Smith (Smith

Here Here in

and and not (

ﬀ . fells fells into )

at at

EoS , price

( . Maximization . He proposed

and and

is the di We disagree with to

with . There is sign erro ect structure criteria

ﬀ is just one of inﬁnite . Utility function, U is

. Function of resource

EoS

)

is wrong because

(

be be known form of -

to molar number to

, resulting that buyer’s total wealth - to entropy,

The The pair

Marshall’s concept of economic s .

, )

ntity , amount of money in this point. We point out that there is E. Smithand D. K. in Foley argued of small country, of of of a yet

)

to (

( ect ect structure of the EoS and

ﬀ as as analogous to the product of pressure and volume (Saslow, 1999)

(Lisman, 1949) (Lisman, at at the initial setting and it is corrected here as follow.

) as mechanical pair but not as resemble of ideal gas EoS.

and total wealth total and

, and commodity qua

, value of money (Smith & Foley, 2008)

as as mechanical pair that the dual analogous

(Saslow, 1999)

of the of ideal EoS gas Saslow (1999) In the work by Saslow J. H. C. Lisman gives analogy of utility, Lisman (1949)Lisman

is analogous to the minus value of Helmholtz free energy,

should not be a mechanical pair in the resemble ideal gas

onsider chemical chemical potential analogous analogous to negative value of internal energy in Saslow analogous to between total utility, total between The surplus is not negative. For least develop economy, 3.3 in neoclassical economics is taken as initial point. Surplus Our Our initial setting comes from e mechanical pair of the Class III of our EoS classiﬁcation. Our e before. never been has and considered is new pairs pairs in nature. It is not necessary to compare or analogy necessary to make analogy of economy to only ideal gas EoS. c Instead one should our thesis, we use ( Smith and Foley general deﬁnition of mechanical pair expenditure expenditure function & Foley, 2008) derived from Legendre transformation of their settings hence they claim th 3.2 constraint is analogous to the conservation of internal energy,

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

. to

)

2 .

( economics economics

. Firstly there is (Mimkes, 2006)

does does not say about

This work does not

. . In this view, wealth is

erential erential forms and with this ﬀ and

)

(

to molar number

(Saslow, 1999)

thermodynamics (2.7), thermodynamics

(Rosser, 2016)

order di

- )

(

)

usion of matter inside system and it deals with only

( ﬀ

inevitably inevitably relies on the concept of entropy and indeed ) is hence minimization of

and and commodity quantity

coordinate coordinate because the EoS is exists in closed and equilibrium

)

are are consumption and investment (assuming no government spending is conserved for reversible process. reversible for is conserved

(

potential describes di

and and

We argue here why it is not appropriate to make analogies of price

pply pply side together, not separately. Saslow Thermodynamics Analogies of Macroeconomics This approach to macroeconomics was proposed by Mimkes (or (or maximizing

A macroeconomic system macroeconomics system is driven by entropy consider any aspect on the EoS either. This thesis considered only micro interest. the sake of further and we mention this work for aspects where where and closed system). Both are expressed in first initial setting, analogous thermodynamical macroeconomics formulation is deducted. The idea begins from noticing that the first law of that the law from begins first noticing idea The macroeconomics, balance of equation capital the similar mathematics as shares 3.4 Chemical internal exchange process, if hence it is used for the analogy, it considers demand side and su EoS. of an the existence no EoS for condition only. Secondly, when considering matter exchange between internal sectors of the system, demand side and supply side should be considered separately. of of as conserved chemical potential

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

, nsidering nsidering the

These analyses .

(Smith & (Smith & Foley, 2008)

nnection nnection between classical (Sousa, 2007)

pair pair are bundles of quantity of between both subjects. between

close close relation between measurement

. and and prices of these commodities (intensive

)

ginalism ginalism of neoclassical economics, marginal rate of r

an an agent in economics system. Formal equivalence of utility and and Santos Costa e. Sousa

ects: are are equal, their is no trade. The ﬁrst law of thermodynamics is the ) takes the role of temperature. When two agents have chance to

Following ma Thermodynamics Thermodynamics View of andConservation Preference General Equilibrium, Constraint ).

Equilibrium determined by a set of state variables a of pair dual by Equilibrium determined in (not necessary closed quantity a system of a Constraint of conservation of in approaching quantity equilibrium state a not to decrease Preference

It It seems that neoclassical economics is mathematically mature and that it does 3.5.1 In the year 2007 to 2008, ﬁne analyses of co Constrained Optimization and General Equilibrium 1) 2) 3)

substitution ( trade if their economics economics is what follows. commodities The (extensive coordinates, mechanical coordinate, Individual Individual is regarded as function and its maximization for each consumer to maximization the entropy are function proposed and its and the second law of thermodynamics version of noticed with three asp with three noticed isolated) and theory physical thermodynamics enjoys.” thermodynamics physical and theory This emphasizes the need of economics. It EoS is suggested in that similarities of formulating economics and thermodynamics thermodynamics are version of analogies analogies or any connection and might give 9 of is quoted page Smith Foley from and It econometrics. new contribution to economics and “Economics, because it does not recognize an equation of intrinsically state in terms or of equilibrium, deﬁne lacks the prices there whether not matter thereanalogies to thermodynamics. However any is might be some additional insights or new signiﬁcant results to obtain from co thermodynamics thermodynamics to neoclassical thermodynamics was shown by Smith (Smith and & Foley Foley, 2008) isomorphism that there is a mathematical proved 3.5

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) ) )

9 26 .4 . .3

3 3 3 3.5) 3.6) 3.7) 3.8)

( ( ( ( ( ( (

under set

multipliers exist,

) spective spective of

)

and and

As one considers

(

is maximized under the

neralized, the constraints

obeying obeying the same constraints

)

To be To be ge

the maximum value exists if

of theof is problem

The function

∑ ( .

and

can can be obtained with Lagrange

(

∑

) (Smith & 2008) (Smith & Foley,

where

equations:

)

(Smith & Foley, 2008; Sousa, 2007)

(

are linearly of Optimal independent. values are

(

for for

ility ility as stated above. The EoS is suggested to relate three variables

erentiable functions

)

(

that is

Constrained Optimization Problem Optimization Constrained

optimization

value di

- (

3.5.2 Mathematical foundation of neoclassical microeconomics and equilibrium

(

and gradient of of all gradient and For real to equivalent are which The The maximized objective function method. This is to solve In maximizing of this function, Lagrangian, maximizing of this function, In Lagrangian, and and some other parameters, constraints constrained behaviors of a system that evolves to maximize a function conditions, constraint of are also function of some value of these variables, thermodynamics thermodynamics can be shown to be isomorphism to each other in the per conservation ofconservation commodities (instead of the internal energy) and the second law is the maximization of ut in a function,

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) - ) ) ) ) 6) 2) 7) 8) 9) 3) 4) 5) 27 1) 10 1 1 1 1 1 1 1 1 1 . .22 .23 . .20 .21 ...... 3 3 3 3 3 3 3 3 3 3 3 3 3 3 (

( ( ( ( ( ( ( ( ( ( ( ( (

here is here

)

, of of composite systems

)

in a process when being

)

) .

)

) )

)

and and

(

Our function Our

)

(

which is denoted with is denoted which

(

( ( (

in this case are in this case

such that the optimal function of entropy entropy of function that the optimal such

)

is maximized to give optimal value

Constrained Optimization in Thermodynamics System in Optimization Constrained Thermodynamics

theis of the entropy maximization

3.5.3 The problem is about maximizing of entropy equilibrium conditions obtained agree with equation (2.19) and they they with equationare and (2.19) agree equilibrium obtained conditions (where

optimal variables, The The The this maximum derived from are variables as Other with constraints: in this case supposing two subsystems, hence two supposing subsystems, in this case Hence

Hence there of exist values Hence optimal The function equilibrium. reached

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) ) ) ) ) )

28 .27 .28 .29 .30 .2 .25 .26

3 3 3 3 3 3 3

( ( ( ( ( ( (

). It is ). It

(in neoclassical

giving giving marginal

ect where where

), (3.

8 ﬀ

), (3.1

7 at at all time is the reversible

at at all time is the reversible

)

) )

ynamics) ynamics) or

)

(in thermod

(

is at maximum, consumer receives additional

(

utility of a customer is maximized, of customer a utility

)

in this case are in this case Changing Considered as Exogenous E as Exogenous Changing Considered

(

with with respect to the coordinate variables,

Optimal function of utility is utility of function Optimal

Constraint Constrained Optimization in Consumer System in Optimization Constrained Consumer

types types of commodity, with consumed quantities,

3.5.5 If constraints of the system are changed, for examples, the total internal energy 3.5.4 For

erentiation erentiation of

ﬀ here

economics) economics) is maximized. When endowment. changes changes or the budget of buying changes, the system moves from point to other point the in such the equilibrium way that A process on a path that utility remains constant at process. The optimal variables, The w The equilibrium conditions are analogous to equations (3.1 equilibrium are conditions The Di utility, with budget constraint: with budget is which (previously denoted as denoted (previously A process on a path that entropy remains constant at process.

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) ) ). of of 29 1

) is .32 .31 o be 1 3 3 ( (3.3 (

ility expenditure expenditure function (Candeal, (Candeal, De Miguel, the consumer, we can

and and temperature (also

hypothesize that exogenous -

hence hence introduced new concept It It is noted that equation (3.3

approach approach that helps guiding us to

) In thermodynamics In concept, an EoS )

odory

(

which which is not the same as equation (

ect. We might pre Carath

intensive intensive variable,

(Sousa, 2007)

ﬀ

, These These two conditions are equivalent to symmetric

(Sousa, 2007)

)

is extensive variable, for an intensive state variable, state intensive for an is extensive variable,

(Smith & Foley, 2008)

In economics, this is economics, In

. (

ect ect structure and ﬀ

Existing of Intensive State Variables and Variables Integrab Existing State Intensive of

In In economics, the constraint is the budget. Changing of budget is changing of 3.5.6 quantity, As consumed ect ect would influence the system via constraints. In this case the constraint is the ff maximized. Proposal Proposal of Smith and Foley EoS into economics. In this thesis, our goal is, as well, to find the EoS, but with our novel concept of e express the EoS from empirical definition of process and to express the variable t according to according Santos Costa e. Sousa must relate extensive variable, intensive) together as can can be built knowing all Walrasian demand functions. known The in economics as Antonelli’s Maxwell’s integratibility condition and the relation second condition is is known as economic integratibility not an EoS in thermodynamics definition. Although it was understood as EoS and and negative semidefinite properties of Hessian matrix of 2001) Mehta, Induráin, & which can be deduced from observations or experiments. This to exist, 1) it must satisfy Maxwell’s relations and 2) The state function optimized obeys behavior of the the system. budget constraint. budget constraint. If the consumer’s budget comes from income of consider the income as exogenous e e

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

Colell, Colell,

- (Mas

at constantat

.” Colell ’s theorem for the and and work term -

)

plane. plane. One and only one

odory in deﬁning a state of the .

XY isolated system from a state . The process is not a thermal pair

Carath hborhood hborhood of any arbitrary initial

thermal processes thermal egion egion in ) in the plane. Hence plane. the ) in

X,Y accessibility

mechanical variable variable is uniquely determined by intensive

his is not the

, t

adiabatic . Family of adiabatic processes constitutes a single rmodynamics. rmodynamics. However the traditional (classical) oncept of thermodynamics based on only entities and : “Processes exist leading to a in : “Processes change exist leading static adiabatic process. static adiabatic odory - é process

static change in a homogenous - it possesses

Carath

. : . The processes shall be dubbed be shall processes . The

Planck Planck postulate laws of thermodynamics) is convenient in along quasi along

- postulated. heat are and necessarily Temperature entities or physical empirical to purely No distinction between

), i.e adiabatic odory Approach plane. plane. To recapitulate, in every neig

mathematical entities.mathematical Empirical DefinitionEntropy ofEmpirical Empirical Definition of a Thermal Process Definitiona Thermal of Empirical

1) 2)

Kelvin - of of a physical system, there exists neighboring states that are not accessible gives gives a strictly logical c constant constant

) to ( -

3.6.2 There is a quasi 3.6.1 Traditional approach of learning and developing of thermodynamics (the Carath The The theorem says that we need a The The work of ,

(Münster, 1970)

parameter parameter family of curves covers completely a r point through passes process each ( adiabatic ( process but an state state state the from Theorem based on experience Theorem non or system in (Buchdahl, 2009; Giles, 1964; Landé, 1926; Münster, 1970) 1926; 2009; Giles, 1964; (Buchdahl, Landé, In a homogenous system, extensive fact is The empirical variable. ﬁrst convex hull in convex geometry as discussed in page 27 of Mas 1989) concepts from empirical variables, e.g. mechanical pairs ( postulated or postulated Clausius introducing basic ideas of the approach fails to follow logical reasoning. These incomplete aspects in its foundation are 3.6

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) ) ) )

)

.36 .33 .34 .35 3 3 3 3

( ( ( ( )), )), which contact to contact

)

(

(3.37)

(

static adiabatic process.

, - )

systems are in thermal are in thermal systems

with the two system, with the newa

and )

)

and

(

exist. To recapitulate, in every

existing ( -

)

( )

means heat exchange allowing

: “If two systems are adiabatically systems adiabatically two : “If are the : “If

, only if the equation, only systems systems are in thermal equilibrium to each

(

)

and and

and (

equilibrium ( )

there are two states of the system with only two adiabatic systems must be in thermal equilibrium to each other. Each (

) essible from the state A along quasi

thermal

known known adiabatic process or an ideal gas which is written as, . If -

and and

)

(

Empirical Deﬁnition of Thermal Equilibrium and Temperature DeﬁnitionThermal ofEmpirical

mechanical mechanical pair) exist separately in equilibrium. If the wall is diathermic

such that such

(

) )

known in text books.

)

3.6.3 Theorem of experience, of andexperience, deﬁnition Theorem Theorem of experience, of andexperience, deﬁnition Theorem

(

is equilibrium to each other and the other, hence the system must have measurable property (with thermometric properties, ( is obeyed. The condition can be attained only by a condition a process.” by be only The thermal attained can is obeyed. is the there If third system or the third phase in co is of experience required, theorem isolated from environment but diathermallyisolated from in other, are they each reversible process of an ideal gas, entropy is constant of process ideal entropy hence an reversible gas, well as neighborhood neighborhood of any arbitrary initial state neighboring A states of acc a physical system, there The exists function s of each state gives deﬁnition of entropy function. For example, in These These two points are of two phases separated by an adiabatic wall. The two (made points of a (allow heat ﬂow), the two points can not co Example is the well through passing them, processes

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) is

( ) ) ) 9 8

40 of of the . .3 .3

, 3 3 3 ( ( (

plane, plane, the ,

work ,

erence between between erence energy

ﬀ

. internal

n state

. The thermal equation of state classical” classical” postulates. According ) “ of

, ( parameter curves in . Temperature scale is expressed if

- or

) : “The same amount of

∫

equation

(

temperature adiabatic pathadiabatic it hence is necessary to have new

thermal ∫

in the second law of r family of single

) .

empirical

is called the is called

is the

( )

absorbed into (or exhausted out of) the system. That is That the system. exhausted out of) intoabsorbed (or

.”

: “For any process initial state, di : “For from to any state ﬁnal (

represents represents anothe

Strictly Statement of the First Law First Statement of the Strictly

∫ )

odory, odory, the first law must be defined with the mechanical pair, i.e. defined

isothermal processes é

( 3.6.4 The above empirical axioms have given us a solid foundation of the zeroth law Deﬁnition Theorem Theorem of experience, and deﬁnition with two reference points or with a reference point and a size of scale. The The The property

for any processes.” any for the increasing (decreasing) in internal energy and work done into (out of) the system the into of) system (out and done in internal energy (decreasing) work the increasing the heat, is called in adiabatic process in adiabatic theIf system evolves along some non definition, work work that change the system is equal to the Hence system. change i given empirically. given necessary to change a system from initial state to final state by adiabatic process. The amount of work is independent of whether or not the system is in equilibrium. The and and the existence of entropy, to Carath with purely empirical concept. Hence the definition of internal energy and heat are family of family function function For examples, for a hydrostatic system, the thermal equation of state is and for a paramagnetics system it is we can define the function can we

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

)

33 )

odory

.4 é

and 3

the EoS.

(

( -

. The ﬁrst . The ﬁrst

uences baseuences

Carath

)

inﬁnite states that obey

for for each adiabatic process

. From here, all classical

and and

, hence the unit of , hence

, hence, implying deﬁnition of

) (

( 3.33 ) )

in the coordinate space of space coordinate in the

. It equivalent to . It

should have the unit of

(

for for adiabatic process. For any process, the axioms. )

) is unit of

odory ( ) as as in equation ( 3.3

) state

)

Carath ( (

). Deﬁnition ). Deﬁnition of temperature as a function of the mechanical

entropic

( 3.

here.

)

is to be checked. is to be odory axioms allows any systems with extensive and intensive

Dimensional unit of Adiabatic accessibility of state means having an an having process adiabatic of means state accessibility Adiabatic equilibriumas is deﬁned Thermal statethermal Having Having a thermal process which is equivalent to having a mechanical ( al al pair (

Application to Other Types ofApplication Other System to

he system can be done. The steps of thought shall follow: steps of system can The he thought done. be 5) 2) 3) 4) 1)

) as natural coordinates manifold the theory’s natural of ) as identiﬁes identiﬁes entropy at empirical variables

The The Carath 3.6.5 The The concept emphasizes on existence of sets of Since Since we have

pair pair is indeed the EoS. Thermodynamics potential is defined on surface Conservation of of Conservation these conditions. This equally implies emphasizing on finding the right coordinates to form mechanic hence EoS is to be found as a constraint surface EoS is to found a constraint be as hence law is to be written. Multiplication of entropy entropy pair ( pair which in turn defines processes processes that are analogous of thermodynamics states and processes. Following the axioms and considering other types of system, mechanical pair and if all analogous steps of one the axiomatic reasoning, can thermodynamics empirically defined a of t analogy coordinates as a mechanical pair to form a first law if there are such states and treatment treatment of thermodynamics have axioms so that empirical theoretical thermodynamics traditional all conseq strong foundation given by derived from the can on and Hence Hence the first law is the equation is the equation law first hence

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

34 ect ect ect the and and

eff

of of eff

class cs, cs, we have neoclassical we we construct the and and T. A. Santos

correspondence correspondence might h variables behave as one -

to - us works, our approach in this . In this scenario, deriving EoS

nomic nomic assumption. Then we use version version of thermodynamical EoS thermodynamics thermodynamics coordinates

ne ne with graphical diagrams

as as and can not inﬂuent other variables.

axiom and, in addition (Smith & Foley, 2008) . We emphasize on ofcharacter variables if

passive

coordinates. We check whic

Unlike all other previo . Carathéodory Carathéodory variables variables of what are erent erent from previous works on thermodynamics analogous

ﬀ . Afterwards, economics’ es the EoS. Having known that the utility must be maximized, key point. key

extensive of the

falls falls into

(Sousa, 2007)

hence EoS is

of the various EoS are characterized with our novel proposal of

and and which variables are The EoS are classiﬁed. This can be do

intensive

thermodynamics potentials(ﬁeld) s

This approach is di . . It is noted that this thesis takes no stand on how to predict more accurately Direction of this thesis In this thesis, we consider analogies between thermodynamics and Our Our approach follows

ect structure analysis with the EoS and we try to identify which built

is EoS by observing naturalness of the EoS from eco eff economics structure structure of variables therefore it might play similar role to entropy maximization in thermodynamics, but to be checked. yet they they are influence Structure structure. disciplines as shown by Smith and Foley Costa e. Sousa thesis clearly distinguish what are 3.7 economics on the grounding that there is mathematical isomorphism between the two number number (or number of particle), charge, mass, magnetic field. In economi units of money, of quantity of goods, number of people (buyers or sellers) and maybe in the later thesis. considered be unit of utility? This is to (in analogy to entropy). We suspect here that the one not be possible. The reason might be that physics is fundamental quantities. richer These than come economics with in units its of length, time, temperature, molar The The first law follows from expression of system a of of economics in which the initial step is about looking for variable that is maximized

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

real real economic phenomena but to build ﬁrst principle framework for what to deduce further to realistic predictability. more to modify and

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

a n

tence tence such as

and and price r postulate Carathéodory

in which whole

properties

be be obtained as how (Buchdahl, 2009; Giles, 1964;

thermometric is an initial trial of the author and

(Gumjudpai, (Gumjudpai, 2018)

he EoS is the ﬁrst key target as suggested by CHAPTER 4 CHAPTER (Gumjudpai, (Gumjudpai, 2018)

OF A MARKET: A WRONG TRIAL WRONG A MARKET: A OF

The existence of t EOS . We shall look at the building blocks of the EoS and afterwards

. to be wrong. For a sake of learning from mistake, this chapter explains how. from of learning this mistake, chapter sake For a to be wrong. The The work in Gumjudpai At a rough glance, in microeconomics system of a market, the equilibrium

s it turn consequence consequence all potentials exist on the EoS surface Münster, 1970) Carathéodory the EoS. constructing as as intensive and extensive quantities. Traditional thermodynamics with fou laws are taken as first principles and EoS should come along Alternative from derivation empirical to fact. thermodynamics was theorized formally by whose theorems suggesting that EoS should exists as the beginning of reasoning, as market market of small economy is a system and equilibrium price can temperature is reached at thermal demand quantity per buyer or equilibrium. per household) and total supply quantity are considered Specific demand quantity (total of of temperature even without its directly measurable nature. Price seems to be similar. very Value of commodities exists due to some assumption and price is formed by agreement in the transaction between sellers and buyers. This motivates trial work i this chapter on the equation of state of the market measured measured directly. We need to measure it via other pressure, volume, electrical potential, electrical resistivity or spectrum of radiation. The zeroth law of classical thermodynamics, which is the founding postulate of the proposessubject, thermal to exist. equilibrium state implies the This directly exis price price is formed by equality of demand and supply quantities. This is very similar to how equilibrium temperature is achieved in thermodynamics. Temperature seem to share some similarity in its definition. Temperature is a function of internal energy and other variables such as pressure or volume, however it can not be

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

), ), as as al. al. 37

)

erent. At ff flow flow are equ - is in equilibrium with

ﬂow ﬂow and out If A is in equilibrium with B - ”. surface surface for a system which is here a

dimensional dimensional -

). Price and temperature are both fundamentally postulated ists a 2 ting theories of the subjects. Price is deﬁned from market

paradigm paradigm of microeconomics should lay foundation of the concepts

cient, cient, perfect competitive and clearing markets A, B, C in which there a a condition when there is no excessive demand or excessive supply ﬃ (

) and price (

The The mechanism of thermal and market equilibriums are quite di We assume there ex First Trial on Setting the Zeroth Law of Thermodynamics Version of Economics duct. duct. We notice here and if we pursue with this initial setup then according to

exchange rate rate equilibrium. exchange and is the character of market that determines if the market equilibrium. of equilibriumothers. This is type the price There are other types of economics equilibrium such as interest rate equilibrium and “For three e are trading of the same and homogenous normal goods. and B is in equilibrium with C, hence A is in equilibrium with C. The gives equilibrium rise to existence of price function which can be ranked from lower to higher does does not stop but still continue with the pro constant equilibrium quantity of bought state may thermodynamics, we classical thermal equilibrium, the heat ﬂow stops or the rate of in If the system is enclosed with heat insulating surface, energy inside constant the and the system system is stays still. At price equilibrium, the buying of commodity such the temperature is deﬁned thermodynamical from thermal equilibrium. The zeroth equilibrium and of price. market of law of market, market, taking into account that three coordinates are quantities supply ( of demand ( to exist before construc equilibrium 4.1

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

38 ) ) ) ) ) ) )

7 1 6 3 4 5 2 ...... 4 4 4 4 4 4 4 ( ( ( ( ( ( (

urve and and the vertical C

Colell et al., 1995; -

upply upply ) S

(Mas

(

rice

inear

of demand and supply supply demandareof and

) )

)

(

( ( urve (b) urve (b)

C supply is curve

(

Linear withLinear Price

The

price elasticityprice

are imaginary. At market clearing price (denoted by by (denoted price clearing market At imaginary. are -

emand emand

Point and

rice

and and The The proportional constant is )

) ) P

and that and

In In the same spirit with the way ideal gas law is formulated, there

f the demand curve is of a function

relations, one ﬁnds

( (

(a). (a).

⁄

inear

(b). 1 . It could be elastic, unitary or inelastic demand depending on which

1 4

. , hence hence ,

(

: (a)

Figure Figure In In a market, i Market withMarket

Figure Figure

Since Since where where Working with these with these Working where as in relation a should be Figure Figure

as in intercept is we consider. the curve of section 4.2 2013) Rubinfeld, & Pindyck

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

39 ) ) ) ) )

(i.e.

inear 9 8 . .

10 11 12 L . . 4 . 4

4 4

4 ( (

( (

(

(b) (b)

. The curve

)

but no vertical

we we ﬁnd,

(

are are forced to be ) ,

1 .

4.2 versus versus 4

(

and and

resulting

)

Linear with Price 6

urve urve .

4 C

(

in equation

)

(

yperbolic

(

in equation

he he hyperbolic slope is

)

, t

9 2

the only change is the change function, demand the only .

4 emand: emand: , 4

here. Note that, Note here.

√ and and from that the slope

( D

4.2

urve

ollowing similar of section procedure ollowing rice rice

F P Figure Figure

)

hence take both imaginary and real values. The inconsistency In In

section

(

upply upply

nitary S

. The slope . The Hence Hence U is linear. is linear.

2 rice rice

. (a) (a)

4 Market with Unitary Price Demand and distinct from In Figure Figure

versus versus

Notice that the slope of supply curve is supply curve that the slope of Notice Using Using this slope and equation unitary) at any points. is slope of hyperbolic curve the hence in as 4.3 Figure Figure comes comes from existence of vertical intercept intercept in condition, by market clearing equal making making in this case. The

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

40 ) ) ) ) ) ) ) per

as 13 14 15 16 17 18 19

...... Hence . Hence

4 4 4 4 4 4 4

( ( ( ( ( ( ( combining combining

demand

)

or or

price

(

in real virial gas which

)

(

and

to its intensive thatquantity is

)

We hence succeed in writing succeed We hence

presents presents analogous surface of ideal gas EoS and

compressibility compressibility factor

( playing playing similar role to the gas constant

)

Figure Figure

(

⁄ is a constant is a constant

) √

modify the modify deﬁnition of is number of household Redeﬁning buyers. is number of

all speciﬁc and speciﬁcall and system.realistic properties of For ideal system

( nd statistical statistical methods. with the speciﬁc property, e.g. encode for real systems the factor is to be found empirically employing sophisticated This makes where a that see we household where In Thermodynamics, the inﬂuence (mechanical force) term is an intensive variable. We shall

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

41 emand (equation

D urface S lastics of lastics of E rice P urface urface (b) S nitary nitary

U imensional D - arket with arket wo M T as as as a EoS of

G deal I (a) EoS of (a) Isothermal Curve (b) Isoprice Curve (a) (b) Curve Isoprice Isothermal (4.18)), a Possible a (4.18)), : : 3 4 . . 4 4 Figure Figure Figure Figure

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

In In 42

the .

erent erent 4 erent. erent. .

ﬀ (b) 4 and and ﬀ

. via . Both are

n should be

ll us the total

are hyperbolic are

erent erent prices do

Figure Figure

ﬀ

ge ge heat and work

by by nature of their Figure Figure

induces induces changes in

n in and and

. In see (Curie (Curie constant) to induce as as

whiles having two di

plane

looks like the ampliﬁcation factor results results in change of

)

erent erent value of is similar to

system where system where . The physical quantities

ﬀ ) by by factor

(

, not to be considered separately as two ,

)

( is an exogenous however di

system, system,

18 . )

ampliﬁed 4

( is

( demand

ect ect of ﬀ price . In case of market with unitary price elasticity of demand, it is

. Here we have explored possibility towards construction of an

comes from the need that

is an exogenous variable of the

, via the EoS,

in the same spirit as isothermal curves

unitary unitary

One One of these variables might not be the correct coordinates. There are nature. nature. E e, e,

are are hypothesized at ﬁrst. Market with linear price elasticity of demand is erent erent curves but instead giving di

n (a) (a) ) ﬀ

itary itary market, intensive inﬂuence . This is that distinct from hydrostat of 4 .

to induce

) We try We to try ﬁnd thermodynamical coordinates of a market. We propose the zeroth Chapter Chapter Conclusion and Critics We also notice that in As we consider equilibrium state, quantity of goods in transactio

erent erent quantities. In simple paramagnetics, magnetic ﬁeld,

. In un ff

( physical physical quantities. From equation for di magnetization are similar i who are both internal agents. Forming an equilibrium price does not te wealth of the market while an forming equilibrium does tell temperature us how much the system energy possesses. internal internal internal (the system) and external (the environment) parts to exchan hence resulting change in internal energy. The situation of market case is di Transactions to form clearing price in a market are completed by buyers and sellers market market is with not give di to each other. denoted denoted with only one single variable, forces of willing to sell and of willing to buy. As a result, one cannot draw a set of isoprice curves Figure possible to derive a constraint surface with an additional to be intensive. considered idea that the demand is ( inconsistent due to market clearing (equilibrium) condition and form Inconsistency of of equation. values of slop 4.4 law such that the price plays the role of temperature. The EoS coordinates

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

43 comings comings of the ) in this chapter will be

)

18 . 4 (

chapter and some additional additional some and critics. chapter

Validity Validity of the proposed EoS (equation EoS for a market and we gain some insights and in future construction. developedhere to proceed paradigm learn some short next in the disproved

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

. A ect is ect ﬀ ect ect is on model model are ﬀ

). As we do as as a set of ciently ciently clear,

ir of variables setup ect eff

ects among the EoS s of an EoS. Truly endogenous endogenous

is way is known as endogenous

erence is the cause the e and erence ﬀ truly ) and intensive coordinate ( ected ected by the others are not clearly stated.

ect ect in th ﬀ

composite function to a set of independent - concept concept of the model is not suff

ect ect must be considered within a pa

known mechanical pairs of EoS are of known mechanical pairs WeEoS are expressed. ect ect structure is expressed in form of a diagram, CHAPTER 5 CHAPTER - ﬀ ects. ects. If ﬀ STRUCTURE DIAGRAM STRUCTURE

g g pattern of truly endogenous eff ECT mapping mapping with non

s EFF ects ects of internal variables existing explicitly in a ) with extensive coordinate (

ics as of the RLC of the ics as circuits. . We analyze on. We analyze how well the rests constant. Cause and eff s to other variables and role of being a In In an EoS, unlike Newton’s or Ohm’s laws, there are three variables, Physical Physical laws have some deeper physical insights that, at present, can not be

ects in some EoS are discussed here so that one can classify types of the known EoS into two classes and the e propose propose a diagram describin variables and propose some criteria to check naturalnes eff it is not easy also to have clear identiﬁcation of which variables are endogenous or exogenous. Therefore we give deﬁnition of independent variable variable keeping keeping effect which is eff change in other variables that are not in the independent variables of the typically known as exogenous eff mathemat temperature ( partial derivative, the cause and e on charge quantity moving through an area. The physical property in the Newton’s law is inertial mass while Similarities the two laws no surprise of that the same shares give vibration mechanical in Ohm’s law the physical property is resistivity. represented represented by the existing mathematical equations. The variables’ role of being the cause In an EoM, for instance, Newton’s second law, force is the cause and the e Similarly in potential di law, Ohm’s the velocity.

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) ) )

1 3 2

. . .

5 5 5 ( ( ( ect ﬀ should look is, all other

(Gumjudpai &

EoS or or in Gumjudpai )

change their values, change an

)

with data obtained from

(

CHAPTER 4

labours, funds, loanable etc.

)

( is endogenous obtain we and is endogenous

)

If )

ects

for for constant values of all the rest variables,

ect on ect

and let there be function, a let there and

ﬀ

of of an EoS. It addresses how +

(

That is That

)

which are considered as the only set of independent

are are said to be exogenous variables and have exogenous

diagram )

( erent types of product, e.g. of product, e.g. types erent novel novel approach to economics employing thermodynamics.

to the model, hence to the

oS status of an empirical relation. Knowing these structures

ﬀ

(

and and disprove it. Having consideration of the EoS of an economics

have have endogenous e

structure (

) )

Thermodynamics Coordinate Variables in anEoS

( are are regarded as constant of the regression. If we change conceptual

ect

This typically happens when ones try to deal Endogenous and ExogenousEndogenous Eff and

)

eff

are are endogenous variables of

value variables,

)

could could lay out some

(

Roles of 5.1.1 Endogenous and exogenous variables are common economics terms. Consider A formal way in describing the classes of EoS is proposed so that we can

(

ect ect on

ﬀ

In In economics, exogenous change is sometimes known as shock of demand or supply of di in markets functions ( framework of the model to include some of example, including exogenous variables to the model, for e some phenomena with a basis of thought that the factors of change that a the model are only variables in framework of the model. When doing regression analys Hence these variables set of real set ( i.e. 5.1 system The results of this chapter bases on Gumjudpai and Setthapramote 2019) Setthapramote, of of the EoS could hint the way to construct other EoS in analogous. In this chapter, we check the naturalness of economics EoS proposed in (Gumjudpai, 2018) namely namely t of consideration. from system a EoS empirically to construct new are a if we like comment and justify the E

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

eld eld . In ﬁ

is an is an

ect ect on

is area

ﬀ

assive assive

(intensive (intensive , ty ty which it

and

. For instance, ,

has a p has

). For ). For examples, in erent erent that . In paramagnetics causes causes the e

(force (force per length). In

ect ect of magnetic in reversible (ideal)

ﬀ

) and

and with constant width which is an electrical energy per is an electrical energy which unit ect, ect, in some cases,

ect ect of pressure

is charge

and and

, that is deﬁned with inﬂuence per unit of ) can take active role, i.e. changing in

. an an external magnetic ﬁeld intensity (instead (instead per unitof of

is (minus sign of pressure). In paramagnetics

is total electric dipole moment

other other cases are slightly diff

are physical of inﬂuence withquantities nature physical are

is the surface tension. In a reversible electrolytic

inciple. Mechanical pair must form a work term,

he he

(that (that is

is T

can can not change unless being an e

is electromotive force is electromotive

(extensive (extensive coordinate). Temperature is a fundamental ect ect on, is the electromotive force ect ect of other inﬂuence that causes changing in

ect ect on. Example of

in motion. where

is energy is per energy unit charge ( and and

) can cause changing changing cause in ) can

. In this case

Intensive Intensive variables Extensive coordinate, Extensive coordinate, eff only endogenous Considering Intensive Y coordinate,

) is dubbed the mechanical pair because they are from the class of can can not change without the eff

is the magnetization Role ofRole Variables

or or . Examples of mechanical pair are such as followed. In hydrostatics

it has eff

1) 2)

is the volume

ect ect of and and

is charge is charge

surface rectangular thin ﬁlm with length 5.1.2 Thermodynamics coordinates are not equivalent although each of them is axis

dimension elastic string,

charge charge quantities to related per unit a of quantity influence has has an endogenous eff quantity cell. electrolytic (as e (as an e.g. force, power or energy but per unit of the quantity or relating quanti role, role, i.e. it takes an eff the volume substance, magnetization intensity, external electric field intensity intensity field electric external a a two cell, of charge. In dielectric substance, system, substance, one thermodynamics thermodynamics coordinate since it is laid by the 0th law of thermodynamics. Pair variables ( physics derived from least action pr of of 3dimensional thermodynamics space. The three variables coordinate) are and

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

. -

47 ) ) ) )

can can

6 4 5 7 ) and . . . .

5 5 5 5

( ( ( (

endogenous

. In case of

ects the volume (that (that is

can can endogenously truly

directly directly but via the but

ect ect .

is electric ﬁeld intensity

) variable variable that is the total

ect ect ﬀ

(

ect ect

. The extensive X is volume ̃

ﬀ

must have both active and and both active must have is

) points from negative to positive

)

and and

can not aff

(

( )

, on that depends on

)

. In dielectrics,

(

where where

( ̃

) can can endogenously a

. In paramagnetics system,

(

can endogenously endogenously a can

the pressure and the pressure aff

and ∑

ect, ect, it should be expressed as special notation of

in a hydrostatic system. in a hydrostatic

. In . elastic In string, ect . Temperature

ﬀ

ects ects

ect ⃗

function

ﬀ

which which is force per area, of of independent variable. For example, we know that

because indeed it is indeed because

o the extensive

to area which which has a spirit of force per magnetic charge (not exist in

has has active role as inﬂuence, it also has passive role, i.e.

)

) and reversely reversely ) and

tells us thermal state of a system. of system. state tells usa thermal is ( endogenous

Temperature, Temperature, T temperature a

ly is related are

s tru

can endogenously can endogenously a 3)

, i.e. which which we deﬁne as a set of independent variable mapping with non

surface surface thin ﬁlm, (that is (that Although Although -

In In this work, we try to ﬁnd a functi Truly Endogenous Eff

ect ect which which is a force per unit charge. Charge is related to . Volume

ﬀ and the other and Instead, Instead, for truly endogenous e for function afterwards. Hence to write a function of of to write EoS function as an Hence a afterwards. sense not make does good composite composite function to a set depends endogenously only on pressure 5.2 variables passive passive roles. In hydrostatic system, reversely a charge. endogenous in cause changes reality) reality) which is related t electric dipole moment hydrostatics system, system, hydrostatics In two paramagnetics,

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

in in

ng 48 ect ect

i ) )

be a

, i.e.

ﬀ 8 9 ected ected . .

5 5 ( ( and and

Expressing Expressing

he he diagrams ther EoS ther . t 1 , O . 1 5 . 5 and so reversely. and so reversely.

ect to the other that

, i.e. having reduc

) ) variables variables and let

Figure Figure

Figure Figure ,

is proportional to ( (

ams In In

and and

propose propose a simple diagrammatic epresentations of

ect pressure ect pressure R ﬀ cause cause to the variable that is aff as

s ects ects of can can a

. In Class I, ﬀ

ect of coordinate variables in the two EoS

ect Structure Diagr Structure ect known. Moreover the known EoS of many other is inversely is proportionalinversely to

)

variable has truly endogenous eff

Temperature Temperature but

( . The reversible electrolytic cell and dielectric substance

ect Structure Diagram for EoS

ect of variables. We hence

EoS are well ff

ect ect to surface surface thin ﬁlm are similar to the hydrostatics system due to their

- Class IEff and Class II Hydrostatics andHydrostatics Paramagnetic

. Situations are reversed in the case of Class II. is an arbitrary magniﬁcation factor to the combined result of

, e.g. for Class I,

) 5.3.2 We analyze truly endogenous eff Proposition of Eff 5.3.1 Hydrostatics (e.g. gases and solids) and paramagnetics systems are two simple

Case Case I: Case Case II:

ect ect to

( as as passive role. We classify them into two classes as in ﬀ represent represent Class I and Class II of EoS. Hydrostatics system is an example of structure in type Class I EoS. e where where having enhancing eff e h hydrostatics EoS and paramagnetics EoS (Curie’s law) in combined of e factor magniﬁcation constant using using arrows connecting from variable that is the by the cause. That is to say one mechanical mechanical work characters are similar to the paramagnetics due to their electromagnetic work characters. Hence, of the twoEoS. of are types representatives good the two systems systems systems of which the systems are similar to either the hydrostatics or the paramagnetics. Systems of elastic string and two 5.3 or or inverse function of these functions. describe The cause truly and endogenous e function does not next.viewpoint

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

. 49 ect

ect can can aff ariables ariables of ower).

the right, for V L can can aff

netic netic system is an ystem ( ystem S ect ect in EoS ff E

aramagnetics aramagnetics P ect ect any other variables. On ndogenous E

pper) and and pper) U ruly T can can not aff

ystem ( ystem S are are written in the diagram. Paramag ected by other variables. other ected by howing howing

ﬀ S

However

and and

and and so reversely. External magnetic ﬁeld intensity

ect ect structure in Class II type EoS. Temperature ydrostatics ydrostatics

H Diagram Diagram can not be a can

1 .

5 ect volume Figure Figure However However can can aff generalization, example of eff magnetization

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

)

is is

) .

truly truly

whether 5

increases increases (

is is of

endogenously. endogenously. is the equation we we hence have

, dictates dictates demand

testing

) and two outgoing

truly

for )

ect are proportional to are ﬀ

ria

, the intensive

can can a

crite equilibrium and the market is

) per number of ( consumer

and and

(

(analogous (analogous to . We try with EoS of a market with with EoS a of market . We try

classiﬁed classiﬁed as the Class III EoS. We 4.3 supply quantity , is the proposed EoS, which are there

EoS 2 of the 0th law of thermodynamics and

of but instead

variables, both variables,

Figure Figure

increases, increases, the price increases

status

ect ect

a ff

is demand quantity is demand ( quantity

The The proposed EoS,

truly truly endogenously but increases the supply The The law states that have

with four arrows. The consequence is that as .

. 5

could

ect diagram employing empirical relation of price mechanism as

Proposed EoS in Section ﬀ increases. increases. As We try We try speciﬁc of case a the school of classical that economics, is the

In In Class I and II diagrams, there are three arrows of the and and it does not a .

ect but the in diagram Figure Figure Written in term of Written of in term

. relation According According to the law, there is no supply surplus left in the market. If

2 . 1) . (Gumjudpai, (Gumjudpai, 2018) ce reduces (Sexton, 2011)

5 is supply is quantity,supply

is the price of commodity. All are measured at ects ects 4.3

) ff With aspects we gain from analysis of roles and relation between coordinate Testing ofTesting a

by by the assumption that price equilibrium is analogous to thermal equilibrium, i.e. 18 empirical

cient and information symmetric. The extensive . Figure Figure

4 exogenously, exogenously, Higher pri quantity only a diagram as in endogenous eff endogenous four arrows. There are two incoming arrows to from arrows Say’s law We shall see whether this equation should be in two follow. criticize points as price price identiﬁes the market’s price equilibrium as of the analogous 0th law. We draw truly endogenous e in eff temperature identiﬁes thermal equilibrium as where where and an unitary price demand and supply as linear function of price as previously proposed in section ( 5.4 variables in an EoS, we will take these aspects as basic

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

, ( )

)

18 ect of ect . 11 . 4 ﬀ 5 ( (

arket with arket endogenous

M the equation ensive ensive

nt rice. On the On the rice. I P truly according according to Say’s

static evolution is a

unction of . This is exogenous e

xtensive and roposed EoS of a EoS of a roposed

E in in the diagram. If we want to ﬁx P dimensional dimensional equilibrium surface

inear ect ect of

, we are left with three arrows as of

ﬀ As a result, As a

is less. The law seems to be wrong but

should be higher. However it does not. .

is not two

upply as upply )

iagram of iagram the

. Combining with the proposed EoS 11 D

, then .

5 endogenous. How supply can increase demand is epresented with the with epresented

ect (

. ff

) E

rrow from truly

emand and emand

and and

D iagram iagram

onsumers have more demand have onsumers

( D

rice P ndogenous . Arrows in the context we propose must be dimensional object. geometrical it Hence is that clear E -

At price equilibrium, At price

nitary nitary ight is the ight oordinates Truly Truly U R C 2) :

2 . the case. We must remember that the e 5

constrained constrained with equation

)

18 . Figure Figure there there is only one degree of freedom left for the system. Quasi process along one 4 but a line. which which is a constraint therefore therefore there should not be an arrow from the diagram by removing the a the Class I and II’s diagrams. Producers then can not inﬂuence the price and become this is and the price not true. less takers. Producing increase does not price because because more production results in more richer hence c consumers income of labour. Labour people are the income to endogenously. endogenously. As we have higher This is because the price is now higher and it is not law must be exogenous, not

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

52 aw, the rrow from L A

and and is not an EoS even

the proposed EoS of a of economics in distinct llowing llowing an

nly a line. nly a A ecause, in Say’s in ecause, Say’s ndogenously. B E price price supply functions proposed in - iagram by by iagram ncepts ncepts of variables. Here we take in - D . We propose diagram presenting truly

iagram. This is xogenously, not xogenously, D aw to the E and and temperature which are variables in an EoS. In

L (Lisman, (Lisman, 1949; Saslow, 1999; Smith & Foley, 2008)

rong rong W emand and and testing of an EoS, of particular interest here, an

D pply Say’s pply Say’s akes a akes ects ects A ff M

ect among these variables so that they can be classiﬁed. This sets a to

ﬀ

’s axiom which concerns much on the existence of the EoS derived from upply upply We found the that proposed EoS is not a new class Trying to Trying S . : 3 . odory 4.3 5

é Chapter Conclusion and Critics We consider major features of thermodynamic coordinate variables of various

therefore the proposed equation is not an EoS surface but o the proposed equation is not an EoS surface therefore market market with unitary price demand and linear section due to the price equilibrium condition which is a constraint condition. The constraint one reduces degree of freedom oneof resulting the only system degree of freedom left which which have initial setting from Carath optimal co empirical facts as initial setting. We found that the EoS can be classes. classified We into two use the concepts we found here in analyzing foundation foundation in constructing economics system. We consider thermodynamics approach ways from other previous works doing doing this, we aim to find a concept central in constructing an EoS from other systems such as an economics system and to find some criteria for judging equation if an could empirical take a status of endogenous e an EoS physical physical systems. We analyze and criticize on roles of these intensive and variables extensive coordinates as they are Figure Figure 5.5

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

)

(

unless with

) . for a system in

) ects) can be ects) can also

(

CHAPTER 4

ect. ect. However .

ﬀ

)

done in done (

side independently from the supply side. We

side EoS which is crucial in studying demand ointing ointing

- . mistakenly )

These come as some novel rules for an empirical ) CHAPTER 6 CHAPTER from causing truly endogenous eff from causing Carlo Carlo simulation in analyzing the demand system.

- ( and and

SIDE EQUATION OF STATE OF EQUATION SIDE ( study study and shall be applied as criteria of the status of an -

ynamical ynamical approach. Next we further formulate the EoS

(apart (apart at at beginning, one can not change value of

ect Structure

(e.g. (e.g. volume) can be independent variable in the equation that

ﬀ of of a system.

might look like exogenous e ect fro

ﬀ

and(or) and(or)

DEMAND , i.e.

)

and and Number of the arrows the three. are of arrows Number is at least one arrow p There Only

( Rules of EoS E Aspects noticed by our In In this chapter, we first set the rules of EoS which are fundamental for further 1) 2) 3)

endogenous e

reality, reality, given a value of truly One One might argue that related so that changing considered as exogenous inﬂuence or a shock or a exogenous inﬂuence as considered EoS, are These considered rules to an EoS. be as relation Our Our view now is to consider the demand market as as do not consider a whole 6.1 analysis. analysis. Next we derive the demand system using formal thermod for a system of consumers in a perfect competitive market. Finally, based on the EoS, we propose how to apply Monte

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

54 asset odory

neither é erent erent from ﬁxed ﬀ Carath

side EoS. It can be - nly one spatial sector. have similar theoretical

is conserved. In price

and erentiation erentiation between empirical

sector but exchangeable. Here ﬀ

and and the ﬁrst law is deﬁned purely

of of valuable assets (e.g. money) is approach approach and use it in building

each

) clear clear di

, odory

é (

. Transfers

is deﬁned with mechanical pair as in equation

Carath

disposable - non Side Economics Version of Thermal ofStates Version Side Thermal Economics - we we do not consider market as a system, but instead we consider

and and

systematic systematic deriving of thermodynamics following Side Equation of State - - Demand Price and Temperature Are Not and Analogous Are Temperature Price

reusable (Buchdahl, (Buchdahl, 2009; Münster, 1970) s.

CHAPTER 4

6.2.2 The system of interest is now a group of consumers in small economy, i.e. the 6.2.1 In this chapter, we notice that, although price In In strictly Demand ), 7 can can not be regarded as temperature. Thermal equilibrium is much di

onsumer onsumer sector as a system and we will construct a demand demand demand side of which the process is to buy only. The which commodity is is a pressure c picturized of internal part of a piston as demand side (buyer) and external part of the piston as supply side (seller) interacting via balancing of internal and external equilibrium, there are two sectors, i.e. consumers and producers (demand side supply and side). Commodities are exchanged with other assets (e.g. money) and of commodities nor money are conserved in unlike origin origin that they are abstract and they identify thermal and price equilibriums, however price equilibrium. In thermal equilibrium, the system has o Energy are exchanged between molecules therefore foundation of thermodynamics formulation of economics. of thermodynamics formulation of foundation such that the EoS is constructed. Internal energy, empirically. Hence existence of the EoS is the beginning step in strictly deriving of thermodynamics. We adopt the facts facts (e.g. pressure, volume) and theoretical entities (e.g. temperature, heat) must be considered. Empirical temperature (3.3 6.2 axioms

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

- e

55 ) )

side - 2 1 . . 6 6 l utility ( ( is molar personal personal

. All these ) static change static change

takes the same -

here here to balance th

) in thermodynamics.

is is the sum of demand

or or . Carathéodory Carathéodory axioms, ) which is analogous to ,

) )

(Saslow, 1999) side economy’s tota and so forth. and -

his is our new deﬁnition and is not the is number of particle and (t

)

. This is similar to monatomic ideal gas that

(

as intensive coordinate intensive coordinate as as extensive coordinate extensive coordinate as whereas whereas ( (

)

static expansion process which is a quasi which is a static expansion process side economy’s total wealth

- -

and (

which which is the work of Saslow

Side Economics Version of Thermal ofEquilibrium Version Side Thermal Economics

3.3

) The The demand

. in perfect competitive market, hence following hence competitivein perfect market, Demand )

(

is the number of consumer or household. Personal total value takes a role of

side microeconomic temperature

- is hence the total wealth per buyer, per the total wealth is hence

6.2.3 In thermodynamics, changing of adiabatic wall to diathermic wall allows heat and and

(

exchanges exchanges and takes the two phases to thermal equilibrium as of of buyers only. Hence there might not be such constants equation. demand number. Economics does not have as many economics, there are units of value (e.g. in fundamental money unit), number of goods and number units as in physics. In wealth where earned earned from using and owning of fixed assets same as in section quantities are the sum of the quantity that each consumer possesses. The Each Each state shall be identified with personal total value ( temperature side economy’s total possession of liquidity asset economy’s (e.g. total possession money) of fixed and assets plus demand demand in thermal economic arbitrary axiom of infinite and make empirical of existence we states, and demand quantities demand and quasi is economic there an If considered considered as energy transfers analogous to the work term ( is therefore, pair mechanical The

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

, -

56 ) ) ) e.g. e.g.

or or to , 3 4 5

. . . scopic scopic

6 6 6

and and the ( ( (

either either fast

zero demand

to lower

rice rice is a marginal

side economics work nly when

er - . ) are allowed averagely O

and and

plays internal role as the same plays energy

likely likely to distribute to everyone

is ready to go to lower temperature so that thermal money money Does Not StopDoes Not But Static.

are are the usages of each group’s all accumulated ﬁxed

here here and in perfect competitive market p

, Market , Market

household Side Economics Version of Version Side Mechanical Work Economics

- is

run money distribution is not transferred by trading but trading by distribution by giving. is run not transferred money -

s A Demand side economy’s total wealth, -

. The long 6.2.5 One needs to be notiﬁed that, in economy, when there is non 6.2.4 Since price, utilize the ﬁxed asset or sh -

the times in a closed piston filled with gas or in a paramagnet. thermal interaction. is no particle's is zero, or magnetization there volume quantity, quantity, there are movements in market’s activity. The buying and selling happen all the times. A market system at static transactions economic or equilibrium exchange contains micro of money and thermodynamics equilibrium, goods there are interactions between microscopic all particles all the times. This is just as at value of transaction is negative (i.e. expense) expense) value transaction is at (i.e. negative of of value should analogously read should analogously Transaction of liquidity asset (e.g. money) of a group of consumers reduces demand side economy’s total wealth (total wealth of the whole consumers) by The demand The law thermodynamics, of first adiabatic hence revenue, revenue, MR which is equal to marginal cost of production, MC. Price takes a role of influence (on buying or selling) per unit of goods. The demand is or slowlyor assets. assets. This situation is like when two groups of people become one bigger Although, group. the liquidity asset (e.g. money) is not yet to share but in long run, as one single family or closed values. values. Heat at higher temperature equilibrium is established. So as economic heat goes from high interpreting as two groups of consumers (each with co

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

57 ect ect ) ) )

ﬀ 8 6 7 . . . 6 6 6 ( ( ( is based on

it is easy to

1 . , 6

)

. is typically inversely

Figure Figure

ect ect demand quantity exchanging exchanging their kinetic analogous to mechanical analogous to mechanical

ﬀ - ,

onomy system, as suggested

. Notice that exogenous e ect

can a

ﬀ 6.1 we propose an EoS, we an propose

side ec

- price,

)

6.1

. Diagram in )

)

can only a can

( (

is constant that is

Personal wealth

( the times exceptthe times when

of of equilibrium are due to two causes of change that

in thermodynamics of a closed system, there are two

s , articles articles are still in interaction 2.2.7 as as required. The diagram is distinct from the Class I and II

and so reversely. so reversely. and

but it is proportional to

and and

ect Structure and Structure Class III EoS ect

ect ect mechanical equilibrium of pressure, (equilibrium mechanical equilibrium (equilibriumthermal of temperature, equilibrium (equilibrium of price

ﬀ ﬀ

Proposing Two Types of Economic Equilibrium TwoProposing Economic Types of E

1) 2) 1)

us that characteristic

can can a

In In thermodynamics when extensive variable is unchanged (e.g. constant 6.2.7 Referring to section 6.2.6 in section and criteria concepts Following ect structure diagram there are two types of two types diagram are equilibrium, ect structure there

equilibrium) which which tell are temperature and pressure. In a closed demand eff by types of of equilibrium: types hence hence it is categorized as Class III. Price proportional proportional to empirical fact and it obeys all rules given in section can come from for or generalization, In perfect competitive market, we know from facts that as written misunderstand misunderstand that all customers stops buying or selling. Indeed, we must consider sellinghappen all and that buying volume or constant magnetization) there are no energy transfer as work term but one must keep in mind that p energy. Hence in economy, when

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

- 58

– erfect

onsumers onsumers in C

. ) roup of as as a case of study. Recall ideal gas

statistical statistical method is employed. As an

, ) ype EoS ype

EoS,

iagram iagram of a

ods in physics to the EoS. To provide numerical

Class III Class III D Carlo simulation.Carlo ( -

ling of Demand Function for Econometrics virial EoS of real gas arket M doing a thought experiment which gives a model of a perfect tructure tructure S by by ncept of thermodynamics, we can define relationship between ect personal wealth equilibrium (equilibrium of personal wealth, wealthpersonal of equilibrium (equilibrium personal Eff

Virial EoSVirial of Gas Real ompetitive : C 2)

1 . 6 6.3.1 Towards a realistic prediction of Using EoS in Mode EoS is empirical law, known in social science as a model. It can be constructed where speciﬁc volume molar where observation observation or (

EoS example, we will take the with or ideal system. That is to say one can have empirical law of a perfect or ideal system world. notreal existthat does in the 6.3 Figure Figure sections, sections, we apply specific meth examination of the EoS and to provide guideline of further economics application, the is the Monte method considered summary summary using co variables of demand system in the light of effect structure application diagram. of thermodynamics This in leads analyzing of to the demand system. In the next two analogous to thermal equilibrium) to thermal analogous These hint us further construction of the first law of thermodynamical economics. In

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) ) see ) ) ) )

(

. The .

14 12 13 11 10

. . . 6 . .

6 6 6 6 6

ling ling and (

( ( ( ( (Gujarati, (

properties

ect ect of time

ling of demand Considering Considering the

s. realistic

due due to mode as

cients

ﬃ

y y endogenous or exogenous.

)

, the factor encode )

pecify pecify assumption of the mode

(

( ̃ ̃

(

side EoS with the Basics ofside EoS EoS with the Basics

oses the concept of EoS in

is an inﬁnite series is an inﬁnite

)

( (

ling, one need to

ect ect to be analyze in the other sets of equation ing of Demand

, as function,as )

ﬀ

7 . are are parameters to be found from regression analysis of data

6 for for the ideal gas. When

( Model

ling ling

Typically Typically )

and and

5.2

Mode

6.3.2 In econometric mode . section of truly endogenous function function as We suppose demand other other exogenous e EoS equation Let us suppose unitary price demand function as truly endogenous function does does not give any insights of which variables are tru What we attain in this thesis prop function. Although it is consider at ﬁxed time equilibrium without the e lagging, it gives a good reason of which variables are the truly endogenous, leaving where where 2009) propose propose a mathematical model. For example, dependency of be proposed as might more precise parameters we have, prediction less using the EoS has less have, and error. parameters we precise more of the gas. of Using data from experiments, one can determine the coe which can be rewritten as can which where

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

)

) ) ) (

17 15 16 . . . 6 6 6 ( ( ( . This has greater in average. There

grows grows with

and and

ersonal procession of of ersonal procession

greater )

of neoclassical of economics. neoclassical Let

that there is no term reﬂecting

erence of p erence

t )

. Moreover

decreases. The decreases. problem exists when )

)

( (

(

)

(

)

and and M )

is the purchasing power. As we consider the

(

, for examples, we might have might examples, we , for

(

here here such that personal liquidity depends on personal

. At greater

diminishing utility marginal

which may not be constant. may which

)

as as parameters of the regression. In this small economy, to be

(

mer’s cash or liquidity is a diff cash mer’s

)

( (

where where In In such model, it is not convenien Consu wealth fraction or liquidity is a constant cash of personal Consumer’s Second exampl Second Third example: First example: First That That is the economy maintains the fraction of liquidity with respect to

y y of ﬁxed assets in the small economy are 2) 2) 3) 1) 1) 2) 1) and and personal possession of ﬁxed asset plus utility earned from using and ) in second term. The sign to more The contributes term. swap in second only. only.

own asset or borrowing)

(

We have to take into account that buying of ﬁxed asset should be less and less e e economy in average, hence it is possible that We assume constancy of

M comparison comparison between the value of utility. does of diminishing concept not follow the marginal hence as as the quantit to the resemble of concept possible look at some a us take models: wealth of assets ﬁxed owning ( wealth total wealth.the economy’s are also variations also modelling of of are where where we use asset liquidity personal value average consumer’s unit of a of a to buy asset, ﬁxed able (money whol

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) )

)

23 20 21 22

61 . . . . 19 ) . 6 6

6 6 6 ( ( ( ( 18 ( . If we .

(

)

erential erential method, we

]

)

ﬀ

It It is straightforward to

) (

erential

ﬀ

Elasticities Elasticities could depend on

(

, we express it as approximated at

)

cs, the total di simple solid

) )

)

(

is is average personal demand. Taking

)

( (

(

side EoS with Total Di cult cult to ﬁt in the framework of econometric

. For -

)

ﬃ

side system. Further we deﬁne Furtherside system. we

[ (

(

is number of consumers in the economy. This is analogous )

as as

)

(

ing of Demand

are are elasticities of demand to personal wealth and demand to price.

where which is still di where where (

cients,

Model

ﬃ

Realistic aspect of data (property) is to be decoded from to is from (property) Realistic decoded of data be aspect

and and

6.3.3 Now we are certain that we have EoS in general form,

here which is the EoS for the is the EoS for demand which In In simplest case, elasticities may be assumed constant other factors as similar to the factors in EoS of write, w Defining coe Defining begin begin with a common method in thermodynami shall express, do not pretend to presume the form of the EoS before hand, but instead we naively regression. logarithm, hence logarithm, to the virial gas in equation order, first

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) ) ) ) )

24 25 26 27 28 . . . . . 62 6 6 6 6 6 ( ( ( ( ( Carlo Carlo - deterministic deterministic - Carlo techniques -

. Carlo simulation of nte -

are are combined to give predicted. Since the input is - also also stochastic behavior. This

e, important contribution is to provide

Carlo Carlo simulation is a non

We can translate the equation which provides guideline to

(Harrison, 2001; Woolfson & Pert, 1999) Pert, & 2001; Woolfson (Harrison,

cases cases we can not find actual data, hence performing Monte of of the each simulation can not be prior

Carlo Simulation of the Demand Function - is an error term.

A process to be modeled with Monte Monte In previous sections, we provide groundwork for interpretation of the demand

way of process is needed of process way random hence the same executions of the simulation do not generate the same the outputs. the same hence executions do not generate simulation random of the Many outputs coming out of statistical many implication executing of processes the considered phenomena. information of probability To or distribution function that the system would perform fall into one the simulation, process. process. The simulation is to imitate real phenomena which is random stochastic. numbers given Input to the is process such that it has means the output economics. economics. In this section, we introduce demand function method as an example. of Procedures in applying Monte of Mo described follow. as are function function that is approached with the EoS. Henc the opportunity in applying thermodynamics for describing market equilibrium in However However in some simulation is useful. 6.4 where link EoS in thermodynamics with regression analysis in econometrics. This enables further applying econometrics methods in analyzing of the EoS in thermodynamics. Our EoS is hence Our model the EoS is hence, econometric for our and

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) )

and and 29 30

. .

6 6 ( (

in market

the consumers) because c c scattering time,

side economic system. side economic - for scattering to state scattering for to state scattering for no scattering. for me step of

)

satisﬁes

)

are

) (

can can be averagely These measured. are time before and and

(

al,

to Theoccur. possible outcomes scattering are to state and and

( side economics system, we do not know such distribution - mechanics, a form of distribution function, e.g. Maxwell

or or state

chosen in the range chosen range in the

they are identic are they each of know properties particles and we response to how other interact they and they to know how each we

Case of Discrete ofCase Discrete Probability Case ofCase Distribution Function or or not being scattered at all. In a ti 1) 2) 3)

Carlo Carlo simulation is plausible for it. The characteristi - Nucleon Nucleon or particles’ scattering processes in physics are stochastic hence 6.4.2 6.4.1 In statistical In In our demand from from initial state to state

Random number number Random probabilities of scattering to state scattering to state of probabilities to scattering state or state Monte consumers consumers are not identical. Properties of each consumer therefore the are way each of not them interacts exactly and responses to known external inﬂuence are not known. Lacking of knowledge about microscopic mechanics of consumers of the demand of mechanics statistical in lacking results external force ﬁeld. force external function (i.e. we do not know microscopic mechanics of function is because known function Boltzmann distribution (or others), can microscopic be characters applied of to the the system. simulation, knowing The particles or molecules’ distribution

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

) )

) ) ) 64 1 2 (in we we

4 5 3 and and

.3 .3

.3 .3 .3

6 6

In In our 6 6 6 ( (

and we ( ( ( have have to

) are are characters

and

and and (in money unit per

and and

) ) (where (where

in a given time step

can be collected and evaluated,

or or change in personal wealth

or or sidering sidering a given time step

At each small fraction of consumed

( (

. where

scattering scattering time,

and and

) )

which which is to be compared with characteristic

research. research. For one unit of changing in price ( (

be be found.

can can

are are measured and averaged experimentally, to these three possibilities.to these three

s the characteristic quantities are the change in consumed quantities of and and , we consider an amount of quantity of goods consumed,

and and

side economics system, instead of con

In In a considered range of In In scattering process, characteristic

where

probability probability of a change in consumed quantity due to the change in price is probability of a change in consumed quantity due to the change in personal wealth is money money unit per unit of good) and changing in personal wealth unit of consumer), if data for therefore Just as be evaluated from surveying compare it with characteristic quantities: compare quantity, goods resulting from either change in price Instead of considering a time step, time, chance chance particles would be scattered into state demand consider a given consumed quantity, Number Number of scattered particles to states 1 and 2 can be simulated using number random shooting of that reﬂect internal properties of the aggregated system. They tell us how much

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

is of

We ).

7 After After

into the

in consumed can can be added ) and (6.2 ) and

the change

(6.2 ,

in consumed quantity is added to

and and

t at the beginning of the

If If the random number falls

and and

random random numbers that fall

can can be se

can hence be simulated by shooting of

satisﬁes

)

is added to and

and

(

is added to

in price or personal wealth.

ected ected only. Therefore change ,

and and ﬀ

)

ect ect structure of variables in physical laws. We use

mber mber falls into the range, depending depending on the value

or or

ossible.

for for change in consumed quantity due wealth. to change in personal for change in consumed quantity due to price change due in consumed change quantity for Carlo Carlo technique could provide application to investigate demand th loop of simulation, chosen in the range chosen range in the

- to these two range of possibilities. Here change

ect ect structure in EoS and propose formal rules to standardize the status

should give the same the predicted by as should the EoS give result

( ’s axiom in formulation of the EoS of the economics system. w economic EoS passes the criteria and is considered as Class III as it

many many markets, especially when there are problems in finding market

competitive market is market competitive proposed is tested and rules proposed with the criteria accumulately simulations, when equilibrium is reached, the equilibrium value

odory The The Monte If If the random nu The The initial values of and and

Chapter Conclusion We conclude eff

in perfect here. The ne Carath consider the eff of an EoS. We classify the EoS into types of diagram. EoS for a group of consumers 6.5 function function in equilibrium based on the standard empirical measurements in economics. This is the case when performing regression analysis or analyzing of general equilibrium model nor neither p easy are into the range, large range, added to must be from only either only change must from be simulation. In an (updated) Consumed quantity due to change in random number quantity are endogenously a Random number number Random

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

- ) 66

(

side economy’s wealth is

methods. At last we propose a method to perform Monte ect ect structure diagram. Total demand ﬀ comes comes with new e considered as internal energy. We study the EoS and construct the function employing econometrics the EoS. simulationCarlo for

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052 work work is

in the other ect structure

ling ling demand d f the rule, we need n thermodynamics n thermodynamics and o be analyze ect ect structure diagram, we to ﬀ

s side economy is found with -

ect

side EoS is of the new class to be ling. ling. Having the EoS helps excluding - side EoS with only truly endogenous -

Carlo Carlo simulation method for the EoS and - of the EoS. In invention o s mode

so so that we have solid tool in deﬁning the a a status of EoS to an empirical equation. This

from the model. Therefore mode

ules and apply the concept of eff

s CHAPTER 7 CHAPTER CONCLUSIONS ogous ogous coordinates. These are personal wealth as endorse axiom hints us to ﬁnd the EoS and all coordinates prior to ’s

odel, odel, leaving other exogenous eff ect ect structure diagram ff e this idea to econometric

truly endogenous function g g analogy of optimal quantities as the beginning step. This is because the the way probability of the simulation is defined. The result of this Carathéodory truly endogenous variable We use There are There two main contributions in this thesis. One is - erent erent theoretical grounds. The EoS for demand ff propose propose variables variables in the m sets of equations. We propose an econometrics model of regression the analysis. EoS We for propose performing Monte regraded as Class as III. regraded of non quantity function must base on the demand di thermal and mechanical anal temperature, price as intensive coordinate. coordinate We have and found that demand the quantity demand as extensive classify classify the EoS into two classes in thermodynamics. Approaching economics in the style of considerin optimal quantities in both disciplines might stand on or might be defined with framework. framework. We apply these new r diagram of the EoS to our proposed EoS. We show that we can use this new concept to disprove the EoS or to advocate the EoS. With the e the other is on thermodynamical formulation of neoclassical economics. In this thesis, we have found new rules to comes with the to define

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

only only at beginning step in deeper investigation concepts. thermodynamical of economics system with further

NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

. . , - n – (1), (1),

3149. – 1380 ,

(4), 1195 bedrijf’and bedrijf’and (1), 12181. . - Hill Inc. 1 - . New York: ,

1144 18), 3145 , . New York: C. –

IX, July IX, . Oxford: Pergamon (17 Hill. - ArXiv ArXiv Preprint Cond

225 ,

Sustainability Journal of EconomicJournal Issues

Proc. 11th Silpakorn University

economics. economics.

. Lucida Bright: McGraw . Bright: Lucida

cs: cs: Conference Series

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Econophysics Econophysics and financial economics: An – . McGraw New York:

300). Berlin, Heidelberg: Springer. Heidelberg: Berlin, 300). – Journal Journal of Physics: Conference Series (1), 233 (1), concepts concepts of classical thermodynamics

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NIDA E-THESIS 5710313001 thesis / recv: 09012563 15:07:41 / seq: 16 306706052

present - 3 BIOGRAPHY Burin Gumjudpai Burin 1996 Mai University Chiang (Physics), B.S. of SussexUniversity 1999 M.Sc. in Physics, of University Portsmouth 2003 Ph.D. in Cosmology, Physics, Naresuan Theoretical Professor of Associate 201 University

EXPERIENCES BIOGRAPHY NAME ACADEMIC BACKGROUND

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