ENERGY, ENTROPY, and INFORMATION Jean Thoma June
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On Entropy, Information, and Conservation of Information
entropy Article On Entropy, Information, and Conservation of Information Yunus A. Çengel Department of Mechanical Engineering, University of Nevada, Reno, NV 89557, USA; [email protected] Abstract: The term entropy is used in different meanings in different contexts, sometimes in contradic- tory ways, resulting in misunderstandings and confusion. The root cause of the problem is the close resemblance of the defining mathematical expressions of entropy in statistical thermodynamics and information in the communications field, also called entropy, differing only by a constant factor with the unit ‘J/K’ in thermodynamics and ‘bits’ in the information theory. The thermodynamic property entropy is closely associated with the physical quantities of thermal energy and temperature, while the entropy used in the communications field is a mathematical abstraction based on probabilities of messages. The terms information and entropy are often used interchangeably in several branches of sciences. This practice gives rise to the phrase conservation of entropy in the sense of conservation of information, which is in contradiction to the fundamental increase of entropy principle in thermody- namics as an expression of the second law. The aim of this paper is to clarify matters and eliminate confusion by putting things into their rightful places within their domains. The notion of conservation of information is also put into a proper perspective. Keywords: entropy; information; conservation of information; creation of information; destruction of information; Boltzmann relation Citation: Çengel, Y.A. On Entropy, 1. Introduction Information, and Conservation of One needs to be cautious when dealing with information since it is defined differently Information. Entropy 2021, 23, 779. -
Lecture 4: 09.16.05 Temperature, Heat, and Entropy
3.012 Fundamentals of Materials Science Fall 2005 Lecture 4: 09.16.05 Temperature, heat, and entropy Today: LAST TIME .........................................................................................................................................................................................2� State functions ..............................................................................................................................................................................2� Path dependent variables: heat and work..................................................................................................................................2� DEFINING TEMPERATURE ...................................................................................................................................................................4� The zeroth law of thermodynamics .............................................................................................................................................4� The absolute temperature scale ..................................................................................................................................................5� CONSEQUENCES OF THE RELATION BETWEEN TEMPERATURE, HEAT, AND ENTROPY: HEAT CAPACITY .......................................6� The difference between heat and temperature ...........................................................................................................................6� Defining heat capacity.................................................................................................................................................................6� -
Chapter 3. Second and Third Law of Thermodynamics
Chapter 3. Second and third law of thermodynamics Important Concepts Review Entropy; Gibbs Free Energy • Entropy (S) – definitions Law of Corresponding States (ch 1 notes) • Entropy changes in reversible and Reduced pressure, temperatures, volumes irreversible processes • Entropy of mixing of ideal gases • 2nd law of thermodynamics • 3rd law of thermodynamics Math • Free energy Numerical integration by computer • Maxwell relations (Trapezoidal integration • Dependence of free energy on P, V, T https://en.wikipedia.org/wiki/Trapezoidal_rule) • Thermodynamic functions of mixtures Properties of partial differential equations • Partial molar quantities and chemical Rules for inequalities potential Major Concept Review • Adiabats vs. isotherms p1V1 p2V2 • Sign convention for work and heat w done on c=C /R vm system, q supplied to system : + p1V1 p2V2 =Cp/CV w done by system, q removed from system : c c V1T1 V2T2 - • Joule-Thomson expansion (DH=0); • State variables depend on final & initial state; not Joule-Thomson coefficient, inversion path. temperature • Reversible change occurs in series of equilibrium V states T TT V P p • Adiabatic q = 0; Isothermal DT = 0 H CP • Equations of state for enthalpy, H and internal • Formation reaction; enthalpies of energy, U reaction, Hess’s Law; other changes D rxn H iD f Hi i T D rxn H Drxn Href DrxnCpdT Tref • Calorimetry Spontaneous and Nonspontaneous Changes First Law: when one form of energy is converted to another, the total energy in universe is conserved. • Does not give any other restriction on a process • But many processes have a natural direction Examples • gas expands into a vacuum; not the reverse • can burn paper; can't unburn paper • heat never flows spontaneously from cold to hot These changes are called nonspontaneous changes. -
Entropy and Life
Entropy and life Research concerning the relationship between the thermodynamics textbook, states, after speaking about thermodynamic quantity entropy and the evolution of the laws of the physical world, that “there are none that life began around the turn of the 20th century. In 1910, are established on a firmer basis than the two general American historian Henry Adams printed and distributed propositions of Joule and Carnot; which constitute the to university libraries and history professors the small vol- fundamental laws of our subject.” McCulloch then goes ume A Letter to American Teachers of History proposing on to show that these two laws may be combined in a sin- a theory of history based on the second law of thermo- gle expression as follows: dynamics and on the principle of entropy.[1][2] The 1944 book What is Life? by Nobel-laureate physicist Erwin Schrödinger stimulated research in the field. In his book, Z dQ Schrödinger originally stated that life feeds on negative S = entropy, or negentropy as it is sometimes called, but in a τ later edition corrected himself in response to complaints and stated the true source is free energy. More recent where work has restricted the discussion to Gibbs free energy because biological processes on Earth normally occur at S = entropy a constant temperature and pressure, such as in the atmo- dQ = a differential amount of heat sphere or at the bottom of an ocean, but not across both passed into a thermodynamic sys- over short periods of time for individual organisms. tem τ = absolute temperature 1 Origin McCulloch then declares that the applications of these two laws, i.e. -
A Simple Method to Estimate Entropy and Free Energy of Atmospheric Gases from Their Action
Article A Simple Method to Estimate Entropy and Free Energy of Atmospheric Gases from Their Action Ivan Kennedy 1,2,*, Harold Geering 2, Michael Rose 3 and Angus Crossan 2 1 Sydney Institute of Agriculture, University of Sydney, NSW 2006, Australia 2 QuickTest Technologies, PO Box 6285 North Ryde, NSW 2113, Australia; [email protected] (H.G.); [email protected] (A.C.) 3 NSW Department of Primary Industries, Wollongbar NSW 2447, Australia; [email protected] * Correspondence: [email protected]; Tel.: + 61-4-0794-9622 Received: 23 March 2019; Accepted: 26 April 2019; Published: 1 May 2019 Abstract: A convenient practical model for accurately estimating the total entropy (ΣSi) of atmospheric gases based on physical action is proposed. This realistic approach is fully consistent with statistical mechanics, but reinterprets its partition functions as measures of translational, rotational, and vibrational action or quantum states, to estimate the entropy. With all kinds of molecular action expressed as logarithmic functions, the total heat required for warming a chemical system from 0 K (ΣSiT) to a given temperature and pressure can be computed, yielding results identical with published experimental third law values of entropy. All thermodynamic properties of gases including entropy, enthalpy, Gibbs energy, and Helmholtz energy are directly estimated using simple algorithms based on simple molecular and physical properties, without resource to tables of standard values; both free energies are measures of quantum field states and of minimal statistical degeneracy, decreasing with temperature and declining density. We propose that this more realistic approach has heuristic value for thermodynamic computation of atmospheric profiles, based on steady state heat flows equilibrating with gravity. -
The Enthalpy, and the Entropy of Activation (Rabbit/Lobster/Chick/Tuna/Halibut/Cod) PHILIP S
Proc. Nat. Acad. Sci. USA Vol. 70, No. 2, pp. 430-432, February 1973 Temperature Adaptation of Enzymes: Roles of the Free Energy, the Enthalpy, and the Entropy of Activation (rabbit/lobster/chick/tuna/halibut/cod) PHILIP S. LOW, JEFFREY L. BADA, AND GEORGE N. SOMERO Scripps Institution of Oceanography, University of California, La Jolla, Calif. 92037 Communicated by A. Baird Hasting8, December 8, 1972 ABSTRACT The enzymic reactions of ectothermic function if they were capable of reducing the AG* character- (cold-blooded) species differ from those of avian and istic of their reactions more than were the homologous en- mammalian species in terms of the magnitudes of the three thermodynamic activation parameters, the free zymes of more warm-adapted species, i.e., birds or mammals. energy of activation (AG*), the enthalpy of activation In this paper, we report that the values of AG* are indeed (AH*), and the entropy of activation (AS*). Ectothermic slightly lower for enzymic reactions catalyzed by enzymes enzymes are more efficient than the homologous enzymes of ectotherms, relative to the homologous reactions of birds of birds and mammals in reducing the AG* "energy bar- rier" to a chemical reaction. Moreover, the relative im- and mammals. Moreover, the relative contributions of the portance of the enthalpic and entropic contributions to enthalpies and entropies of activation to AG* differ markedly AG* differs between these two broad classes of organisms. and, we feel, adaptively, between ectothermic and avian- mammalian enzymic reactions. Because all organisms conduct many of the same chemical transformations, certain functional classes of enzymes are METHODS present in virtually all species. -
Thermodynamics
ME346A Introduction to Statistical Mechanics { Wei Cai { Stanford University { Win 2011 Handout 6. Thermodynamics January 26, 2011 Contents 1 Laws of thermodynamics 2 1.1 The zeroth law . .3 1.2 The first law . .4 1.3 The second law . .5 1.3.1 Efficiency of Carnot engine . .5 1.3.2 Alternative statements of the second law . .7 1.4 The third law . .8 2 Mathematics of thermodynamics 9 2.1 Equation of state . .9 2.2 Gibbs-Duhem relation . 11 2.2.1 Homogeneous function . 11 2.2.2 Virial theorem / Euler theorem . 12 2.3 Maxwell relations . 13 2.4 Legendre transform . 15 2.5 Thermodynamic potentials . 16 3 Worked examples 21 3.1 Thermodynamic potentials and Maxwell's relation . 21 3.2 Properties of ideal gas . 24 3.3 Gas expansion . 28 4 Irreversible processes 32 4.1 Entropy and irreversibility . 32 4.2 Variational statement of second law . 32 1 In the 1st lecture, we will discuss the concepts of thermodynamics, namely its 4 laws. The most important concepts are the second law and the notion of Entropy. (reading assignment: Reif x 3.10, 3.11) In the 2nd lecture, We will discuss the mathematics of thermodynamics, i.e. the machinery to make quantitative predictions. We will deal with partial derivatives and Legendre transforms. (reading assignment: Reif x 4.1-4.7, 5.1-5.12) 1 Laws of thermodynamics Thermodynamics is a branch of science connected with the nature of heat and its conver- sion to mechanical, electrical and chemical energy. (The Webster pocket dictionary defines, Thermodynamics: physics of heat.) Historically, it grew out of efforts to construct more efficient heat engines | devices for ex- tracting useful work from expanding hot gases (http://www.answers.com/thermodynamics). -
Information Across the Ecological Hierarchy
entropy Opinion Information Across the Ecological Hierarchy Robert E. Ulanowicz 1,2 1 Department of Biology, University of Florida, Gainesville, FL 32611-8525, USA; [email protected]; Tel.: +1-352-378-7355 2 Center for Environmental Science, University of Maryland, Solomons, MD 20688-0038, USA Received: 17 July 2019; Accepted: 25 September 2019; Published: 27 September 2019 Abstract: The ecosystem is a theatre upon which is presented, in various degrees and at differing scales, a drama of constraint and information vs. disorganization and entropy. Concerning biology, most think immediately of genomic information. It strongly constrains the form and behavior of individual species, but its influence upon community structure is indeterminate. At the community level, information acts as a formal cause behind regular patterns of development. Community structure is an amalgam of information and entropy, and the Gibbs–Boltzmann formula departs from the thermodynamic sense of entropy. It measures only the extreme that entropy might reach if the elements of the system were completely independent. A closer analogy to physical entropy in systems with interactions is the conditional entropy—the amount by which the Shannon measure is reduced after the information in the constraints among elements has been subtracted. Finally, at the whole ecosystem level, in communities that inhabit mostly fixed physical environments (e.g., landscapes or seabeds), the distributions of plants and animals appear to be independent both of causal mechanisms and trophic controls, and assume instead forms that maximize the overall entropy of dispersal. Keywords: centripetality; conditional entropy; entropy; information; MAXENT; mutual information; network analysis 1. Genomic Information Acts Primarily on Organisms Information plays different roles in ecology at various scales, and the goal here is to characterize and compare those disparate actions. -
Entropy and Negentropy Principles in the I-Theory
Journal of High Energy Physics, Gravitation and Cosmology, 2020, 6, 259-273 https://www.scirp.org/journal/jhepgc ISSN Online: 2380-4335 ISSN Print: 2380-4327 Entropy and Negentropy Principles in the I-Theory H. H. Swami Isa1, Christophe Dumas2 1Global Energy Parliament, Trivandrum, Kerala, India 2Atomic Energy Commission, Cadarache, France How to cite this paper: Isa, H.H.S. and Abstract Dumas, C. (2020) Entropy and Negentropy Principles in the I-Theory. Journal of High Applying the I-Theory, this paper gives a new outlook about the concept of Energy Physics, Gravitation and Cosmolo- Entropy and Negentropy. Using S∞ particle as 100% repelling energy and A1 gy, 6, 259-273. particle as the starting point of attraction, we are able to define Entropy and https://doi.org/10.4236/jhepgc.2020.62020 Negentropy on the quantum level. As the I-Theory explains that repulsion Received: January 31, 2020 force is driven by Weak Force and attraction is driven by Strong Force, we Accepted: March 31, 2020 also analyze Entropy and Negentropy in terms of the Fundamental Forces. Published: April 3, 2020 Keywords Copyright © 2020 by author(s) and Scientific Research Publishing Inc. I-Theory, I-Particle, Entropy, Negentropy, Syntropy, Intelligence, Black Matter, This work is licensed under the Creative White Matter, Red Matter, Gravitation, Strong Force, Weak Force, Free Energy Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access 1. Introduction In a previous article entitled “I-Theory—a Unifying Quantum Theory?” [1], the authors introduced the I-Theory as a unifying theory. -
What Is Quantum Thermodynamics?
What is Quantum Thermodynamics? Gian Paolo Beretta Universit`a di Brescia, via Branze 38, 25123 Brescia, Italy What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? For everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. How- ever, as already recognized by Schr¨odinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism of ordinary quantum theory, so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility, we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior) and maximal-entropy-generation non-equilibrium dynamics. In this long introductory paper we discuss the background and formalism of Quantum Thermo- dynamics including its nonlinear equation of motion and the main general results regarding the nonequilibrium irreversible dynamics it entails. -
Lecture 6: Entropy
Matthew Schwartz Statistical Mechanics, Spring 2019 Lecture 6: Entropy 1 Introduction In this lecture, we discuss many ways to think about entropy. The most important and most famous property of entropy is that it never decreases Stot > 0 (1) Here, Stot means the change in entropy of a system plus the change in entropy of the surroundings. This is the second law of thermodynamics that we met in the previous lecture. There's a great quote from Sir Arthur Eddington from 1927 summarizing the importance of the second law: If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equationsthen so much the worse for Maxwell's equations. If it is found to be contradicted by observationwell these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of ther- modynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Another possibly relevant quote, from the introduction to the statistical mechanics book by David Goodstein: Ludwig Boltzmann who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. There are many ways to dene entropy. All of them are equivalent, although it can be hard to see. In this lecture we will compare and contrast dierent denitions, building up intuition for how to think about entropy in dierent contexts. The original denition of entropy, due to Clausius, was thermodynamic. -
Similarity Between Quantum Mechanics and Thermodynamics: Entropy, Temperature, and Carnot Cycle
Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle Sumiyoshi Abe1,2,3 and Shinji Okuyama1 1 Department of Physical Engineering, Mie University, Mie 514-8507, Japan 2 Institut Supérieur des Matériaux et Mécaniques Avancés, 44 F. A. Bartholdi, 72000 Le Mans, France 3 Inspire Institute Inc., Alexandria, Virginia 22303, USA Abstract Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the quantity of heat, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one. PACS number(s): 03.65.-w, 05.70.-a 1 In their work [1], Bender, Brody, and Meister have developed an interesting discussion about a quantum-mechanical analogue of the Carnot engine. They have treated a two-state model of a single particle confined in a one-dimensional potential well with width L and have considered reversible cycle. Using the “internal” energy, E (L) = ψ H ψ , they define the pressure (i.e., the force, because of the single dimensionality) as f = − d E(L) / d L , where H is the system Hamiltonian and ψ is a quantum state. Then, the analogue of “isothermal” process is defined to be f L = const.