DOCSLIB.ORG

Restricted Agents in Thermodynamics and Quantum Information Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Restricted Agents in Thermodynamics and Quantum Information Theory Research Collection Doctoral Thesis Restricted agents in thermodynamics and quantum information theory Author(s): Krämer Gabriel, Lea Philomena Publication Date: 2016 Permanent Link: https://doi.org/10.3929/ethz-a-010858172 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library Diss. ETH No. 23972 Restricted agents in thermodynamics and quantum information theory A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich) presented by Lea Philomena Kr¨amer Gabriel MPhysPhil, University of Oxford born on 18th July 1990 citizen of Germany accepted on the recommendation of Renato Renner, examiner Giulio Chiribella, co-examiner Jakob Yngvason, co-examiner 2016 To my family Acknowledgements First and foremost, I would like to thank my thesis supervisor, Prof. Renato Renner, for placing his trust in me from the beginning, and giving me the opportunity to work in his group. I am grateful for his continuous support and guidance, and I have always benefited greatly from the discussions we had | Renato without doubt has a clear vision, a powerful intuition, and a deep understanding of physics and information theory. Perhaps even more importantly, he has an exceptional gift for explaining complex subjects in a simple and understandable way. I would also like to thank my co-examiners Giulio Chiribella and Jakob Yngvason for agreeing to be part of my thesis committee, and for their input and critical questions in the discussions and conversations we had. Here in Zurich, I primarily want to thank the members of the Quantum Information Group, and the whole of the ITP, for the many enjoyable moments we shared in the last five years; from coffee breaks to intensive exam marking sessions, I have always felt part of a great community that held together and watched out for each other, and I am sure that the bonds and friendships we formed will last for a long time to come. In particular, I am very grateful for the “coffee office” of Caterina, Gizem, and Simone, for the cakes by Aleks and with Reimar, Sandra, Luca, Paolo and others, for the greek coffees with Philippe, and for the many things I learnt during teaching assistance with and from Babis, Manfred and Renato. I want to mention also earlier members of the group, such as Marco, Fr´ed,Cyril, Roger, Johan, Fernando, Norm and Mario Ziman, and members of the Computational Physics group like Tama and Andreas, who have contributed greatly to the welcoming atmosphere I felt at the beginning of my PhD. I would like to give special thanks to Philippe and L´ıdia,my office mates during most of my PhD, who have worked with me on the projects related to this thesis. I have learnt a lot from them, and always enjoyed discussing research | this also applies to Mirjam, who it was always a great pleasure to work with, and to other members of our group like Joe, Sandra, Rotem, Daniela, Christopher and David. Likewise, I have benefited greatly from discussions with members of the wider Quantum Information community at a number of conferences, in particular Jens Eisert, David Jennings, Tobias Fritz, Barry Sanders, Bob Coecke, Dominik Janzing, Ralph, Yelena, Jonathan and Priyaa. Thanks also to L´ıdia,Gilles and Philipp for their feedback on earlier drafts of this thesis, and for the many discussions throughout my PhD. I would also like to thank my new colleagues at JB, who have made me feel extremely welcome at my new job during the critical overlapping first, or last, month of work. Looking back at the past five years, I am also immensely grateful to my friends both at ETH and outside, who have filled my life in Zurich with joy and supported me in difficult times. To this end, I would like to thank my close friend and first Zurich flatmate Ellen, who already studied with me in Oxford, and who really gave me the idea of coming to Zurich. I would also like to thank Lena, my other flatmate and almost-colleague, for her friendship and the many ice creams we had together on sunny days on Hoenggerberg. I am also immensely grateful to my \Br¨uderchen", v friend, dance partner and flatmate Vassili, to my incredible and beloved all-round friend L´ıdia,and to my friends Yasmine, Gilles, Alexejs, crazy Rinat, Manos Cop- perfield (my wine expert who can cook even without onions), who have really made my time in Zurich. The same is true for the Zurich Tango community, and in partic- ular the people of Cuartito Azul, such as Angela, Philip, Alexey, Jorge, Diego and Soledad, Tomas and the Cafet´ınde Buenos Aires, Pablo from El Social, Marcello, Chiara and the other Mates, Olga, Markus, Javier & Rahel, Silvana, Mozzarella and Andrea, Alessandro, Jackie and many more, as well as the Flamenco cajon group. I would also like to thank my friends from before Zurich, such as Lam, Neven, Karl, Hans, Alex & Martha, and in particular Fanny, who have all continued to take part in my life here. Thanks also to the welcoming staff and owners of Caf´eHoengg and Caf´eMiyuko, where parts of this thesis were written. Most importantly, I would like to thank my family, both old and new, in Germany, Hong Kong and Brazil, to whom this thesis is really dedicated | every part of this thesis belongs to you, and would not have been possible without you. It is an incredible blessing to have you all | Nissar, Mama, Papa, Till, IC, Oma, Opa, Kitty, Gotti, Gotti Gila, Gisela, Gottfried, Klaus, Uschi, Mae, Thais, Rodrigo, Martha, Daniel, Marina, Alexia, In´acio,e todo o resto da nossa grande familia! vi Abstract A simple yet powerful way to address most questions in physics and information theory is to ask: \What is possible, and what is impossible, for an agent operating under a given set of constraints? And what would become possible if the agent had access to an additional set of resources?" This idea is at the heart of resource theo- ries, a tool that was first introduced in quantum information theory in the context of entanglement theory, where it gave rise to the well-known concepts of entanglement of formation and distillation, and has found many applications since. For example, thermodynamics has long been understood as a theory that imposes fundamental constraints, like the second law of thermodynamics. Generalising this idea, resource theories of quantum thermodynamics have now shown that microscopic processes are governed by a whole family of second laws, which involve single-shot entropies known from information theory. While resource theories have greatly advanced our understanding of many areas in physics, there are a few important aspects that have not yet been addressed explicitly within existing resource theories; it is the main aim and contribution of this thesis to fill these gaps. The first aspect concerns the subjective knowledge of agents. In quan- tum information theory, this is normally represented by means of density matrices | this does not admit approximate descriptions, coarse-grained descriptions such as specifying a few observable properties, or other kinds of non-probabilistic knowledge. This in particular implies that resource theories cannot study exactly how lack of knowledge influences the way that agents may exploit resources. The second aspect is that current resource theories cannot model the way that different agents interact and perceive each other's actions. Resource theories are lacking tools to include sev- eral agents within the same framework, who may differ in their knowledge and their language to describe resources, such as a macroscopic observer and a microscopic \demon" in the Maxwell demon thought experiment. The final aspect concerns the understanding of subsystems and the composition of resources, as well as the way that one can quantify resources and the cost of transformations. Current resource theories pursue a bottom-up-approach: individual resources can be composed with the tensor product, and resources are quantified in terms of copies of resources and their asymptotic conversion rates. However, with such a model one cannot capture situations in which there are unknown correlations between subsystems | likewise, resource theories are lacking tools to quantify resources in the single-shot regime. This thesis develops the missing tools to address these issues and formalises subjec- tive knowledge as well as the interaction of different agents in resource theories. vii viii Kurzfassung Ein einfacher und doch vielversprechender Weg, die meisten Probleme der Physik und Informationstheorie anzugehen, ist, zu fragen: \Was ist m¨oglich, und was unm¨oglich, wenn man unter gewissen Restriktionen arbeitet? Und was k¨onnte man erreichen, wenn man noch zus¨atzliche Ressourcen zur Verf¨ugungh¨atte?" Diese Idee liegt den sogenannten Ressourcentheorien zugrunde. Ressourcentheo- rien wurden in der Quanteninformationstheorie als Erstes im Zusammenhang der Verschr¨ankungdurch die LOCC-Theorie betrachtet, welche die ber¨uhmten Ver- schr¨ankungsmasseder `entanglement of formation' und des `distillable entanglement' einf¨uhrte| Ressourcentheorien allgemein werden bis heute in vielen Bereichen mit grossem Erfolg angewandt. Ein Beispiel hierf¨urliefert die Thermodynamik, welche lange schon als eine Theorie verstanden wurde, die uns fundamentale Grenzen setzt, wie etwa das zweite Gesetz der Thermodynamik. Nun konnten Ressourcentheorien f¨urQuanten-Thermodynamik zeigen, dass f¨urmikroskopische Prozesse eine ganze Familie von \zweiten Haupts¨atzen"gelten, die sich mit Hilfe von sogenannten Single- shot Entropien, die wir aus der Informationstheorie kennen, ausdr¨ucken lassen. Obwohl Ressourcentheorien unser Verst¨andnisin vielen Bereichen der Physik und Informationstheorie erweitert haben, gibt es eine Reihe wichtiger Aspekte, die bisher noch nicht explizit von Ressourcentheorien formalisiert wurden oder ¨uberhaupt for- malisierbar waren | diese Aspekte zu beschreiben ist das Hauptziel, und der gr¨osste Beitrag, dieser Dissertation.
Load more

Recommended publications
  • Quantum Biology: an Update and Perspective
    quantum reports Review Quantum Biology: An Update and Perspective Youngchan Kim 1,2,3 , Federico Bertagna 1,4, Edeline M. D’Souza 1,2, Derren J. Heyes 5 , Linus O. Johannissen 5 , Eveliny T. Nery 1,2 , Antonio Pantelias 1,2 , Alejandro Sanchez-Pedreño Jimenez 1,2 , Louie Slocombe 1,6 , Michael G. Spencer 1,3 , Jim Al-Khalili 1,6 , Gregory S. Engel 7 , Sam Hay 5 , Suzanne M. Hingley-Wilson 2, Kamalan Jeevaratnam 4, Alex R. Jones 8 , Daniel R. Kattnig 9 , Rebecca Lewis 4 , Marco Sacchi 10 , Nigel S. Scrutton 5 , S. Ravi P. Silva 3 and Johnjoe McFadden 1,2,* 1 Leverhulme Quantum Biology Doctoral Training Centre, University of Surrey, Guildford GU2 7XH, UK; [email protected] (Y.K.); [email protected] (F.B.); e.d’[email protected] (E.M.D.); [email protected] (E.T.N.); [email protected] (A.P.); [email protected] (A.S.-P.J.); [email protected] (L.S.); [email protected] (M.G.S.); [email protected] (J.A.-K.) 2 Department of Microbial and Cellular Sciences, School of Bioscience and Medicine, Faculty of Health and Medical Sciences, University of Surrey, Guildford GU2 7XH, UK; [email protected] 3 Advanced Technology Institute, University of Surrey, Guildford GU2 7XH, UK; [email protected] 4 School of Veterinary Medicine, Faculty of Health and Medical Sciences, University of Surrey, Guildford GU2 7XH, UK; [email protected] (K.J.); [email protected] (R.L.) 5 Manchester Institute of Biotechnology, Department of Chemistry, The University of Manchester,
    [Show full text]
  • Bluff Your Way in the Second Law of Thermodynamics
    Bluff your way in the Second Law of Thermodynamics Jos Uffink Department of History and Foundations of Science Utrecht University, P.O.Box 80.000, 3508 TA Utrecht, The Netherlands e-mail: uffi[email protected] 5th July 2001 ABSTRACT The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-(a)symmetry and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Caratheodory´ and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-asymmetry plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. KEY WORDS: Thermodynamics, Second Law, Irreversibility, Time-asymmetry, Arrow of Time. 1 INTRODUCTION There is a famous lecture by the British physicist/novelist C. P. Snow about the cul- tural abyss between two types of intellectuals: those who have been educated in literary arts and those in the exact sciences. This lecture, the Two Cultures (1959), characterises the lack of mutual respect between them in a passage: A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have 1 with considerable gusto been expressing their incredulity at the illiteracy of sci- entists.
    [Show full text]
  • A Scientific Metaphysical Naturalisation of Information
    1 A Scientific Metaphysical Naturalisation of Information With a indication-based semantic theory of information and an informationist statement of physicalism. Bruce Long A thesis submitted to fulfil requirements for the degree of Doctor of Philosophy Faculty of Arts and Social Sciences The University of Sydney February 2018 2 Abstract The objective of this thesis is to present a naturalised metaphysics of information, or to naturalise information, by way of deploying a scientific metaphysics according to which contingency is privileged and a-priori conceptual analysis is excluded (or at least greatly diminished) in favour of contingent and defeasible metaphysics. The ontology of information is established according to the premises and mandate of the scientific metaphysics by inference to the best explanation, and in accordance with the idea that the primacy of physics constraint accommodates defeasibility of theorising in physics. This metaphysical approach is used to establish a field ontology as a basis for an informational structural realism. This is in turn, in combination with information theory and specifically mathematical and algorithmic theories of information, becomes the foundation of what will be called a source ontology, according to which the world is the totality of information sources. Information sources are to be understood as causally induced configurations of structure that are, or else reduce to and/or supervene upon, bounded (including distributed and non-contiguous) regions of the heterogeneous quantum field (all quantum fields combined) and fluctuating vacuum, all in accordance with the above-mentioned quantum field-ontic informational structural realism (FOSIR.) Arguments are presented for realism, physicalism, and reductionism about information on the basis of the stated contingent scientific metaphysics.
    [Show full text]
  • Constructor Theory of Thermodynamics
    Constructor Theory of Thermodynamics Chiara Marletto1 Materials Department, University of Oxford July 2016 The laws of thermodynamics, powerful for countless purposes, are not exact: both their phenomenological and their statistical-mechanical versions are valid only at ‘macroscopic scales’, which are never defined. Here I propose a new, exact and scale-independent formulation of the first and second laws of thermodynamics, using the principles and tools of the recently proposed constructor theory. Specifically, I improve upon the axiomatic formulations of thermodynamics (Carathéodory, 1909; Lieb & Yngvason, 1999) by proposing an exact and more general formulation of ‘adiabatic accessibility’. This work provides an exact distinction between work and heat; it reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second); it resolves the clash between the irreversibility of the ‘cycle’-based second law and time-reversal symmetric dynamical laws. It also achieves the long-sought unification of the axiomatic version of the second law with Kelvin’s. 1. Introduction An insidious gulf separates existing formulations of thermodynamics from other fundamental physical theories. Those formulations are approximate and scale-dependent – i.e., they have only a certain domain of applicability, or hold only at a certain ‘scale’, or level of ‘coarse-graining’, none of which are ever specified. So existing thermodynamics can provide powerful predictions and explanations of ‘macroscopic’ systems such as Victorian heat engines, but not 1 Address for correspondence: [email protected] 1 about ‘microscopic’ ones, such as individual quantum systems. Consequently, the conventional wisdom is that thermodynamics is not a fundamental theory of physics at all.
    [Show full text]
  • The Physics and Mathematics of the Second Law of Thermodynamics
    THE PHYSICS AND MATHEMATICS OF THE SECOND LAW OF THERMODYNAMICS Elliott H. Lieb∗ Departments of Physics and Mathematics, Princeton University Jadwin Hall, P.O. Box 708, Princeton, NJ 08544, USA Jakob Yngvason ∗∗ Institut f¨ur Theoretische Physik, Universit¨at Wien, Boltzmanngasse 5, A 1090 Vienna, Austria Abstract: The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence, states that given any two states of the same chemical composition at least one is adiabatically accessible from the other) and we show that it can be derived from some assumptions about the pressure and thermal equilibrium. Temperature is derived from entropy, but at the start not even the concept of ‘hotness’ is assumed. Our formulation offers a certain clarity and rigor that goes beyond most textbook discussions of the second law. 1998 PACS: 05.70.-a Mathematical Sciences Classification (MSC) 1991 and 2000: 80A05, 80A10 arXiv:cond-mat/9708200v2 [cond-mat.soft] 28 Jan 1999 This paper is scheduled to appear in Physics Reports 310, 1-96 (1999) ∗ Work partially supported by U.S. National Science Foundation grant PHY95-13072A01. ∗∗ Work partially supported by the Adalsteinn Kristjansson Foundation, University of Iceland. c 1997 by the authors. Reproduction of this article, by any means, is permitted for non-commercial purposes.
    [Show full text]
  • Ambiguities in Order-Theoretic Formulations of Thermodynamics
    Ambiguities in order-theoretic formulations of thermodynamics Robert Marsland III (Physics of Living Systems Group, Massachusetts Institute of Technology), Harvey R. Brown (Faculty of Philosophy, University of Oxford) Giovanni Valente (Department of Philosophy, University of Pittsburgh) Abstract Since the 1909 work of Carath´eodory, formulations of thermodynam- ics have gained ground which highlight the role of the the binary re- lation of adiabatic accessibility between equilibrium states. A feature of Carath´edory'ssystem is that the version therein of the second law contains an ambiguity about the nature of irreversible adiabatic processes, making it weaker than the traditional Kelvin-Planck statement of the law. This paper attempts first to clarify the nature of this ambiguity, by defining the arrow of time in thermodynamics by way of the Equilibrium Principle (\Minus First Law"). It then argues that the ambiguity reappears in the important 1999 axiomatisation due to Lieb and Yngvason. 1 Introduction A number of attempts in recent decades to put equilibrium thermodynamics on a rigorous conceptual and mathematical footing have been been influenced by the 1909 work of Constantin Carath´eodory1. A prominent example is that due to Elliott Lieb and Jacob Yngvason, in a lengthy paper published in 19992. These authors follow Carath´eodory in basing their approach on the notion of adiabatic accessibility, but do without the machinery of differential forms that Carath´eodory had used in his reasoning. A penetrating analysis of the Lieb- Yngvason formulation was published by Jos Uffink in 2001, principally with a view to determining which axioms proposed by these authors were time sym- metric and which not.3 In the present paper, we are concerned with a related but distinct issue.
    [Show full text]
  • Toward a Computational Theory of Everything
    International Journal of Recent Advances in Physics (IJRAP) Vol.9, No.1/2/3, August 2020 TOWARD A COMPUTATIONAL THEORY OF EVERYTHING Ediho Lokanga A faculty member of EUCLID (Euclid University). Tipton, United Kingdom HIGHLIGHTS . This paper proposes the computational theory of everything (CToE) as an alternative to string theory (ST), and loop quantum gravity (LQG) in the quest for a theory of quantum gravity and the theory of everything. A review is presented on the development of some of the fundamental ideas of quantum gravity and the ToE, with an emphasis on ST and LQG. Their strengths, successes, achievements, and open challenges are presented and summarized. The results of the investigation revealed that ST has not so far stood up to scientific experimental scrutiny. Therefore, it cannot be considered as a contender for a ToE. LQG or ST is either incomplete or simply poorly understood. Each of the theories or approaches has achieved notable successes. To achieve the dream of a theory of gravity and a ToE, we may need to develop a new approach that combines the virtues of these two theories and information. The physics of information and computation may be the missing link or paradigm as it brings new recommendations and alternate points of view to each of these theories. ABSTRACT The search for a comprehensive theory of quantum gravity (QG) and the theory of everything (ToE) is an ongoing process. Among the plethora of theories, some of the leading ones are string theory and loop quantum gravity. The present article focuses on the computational theory of everything (CToE).
    [Show full text]
  • FOOTPRINTS of GENERAL SYSTEMS THEORY Aleksandar Malecic Faculty of Electronic Engineering University of Nis, Serbia Aleks.Maleci
    FOOTPRINTS OF GENERAL SYSTEMS THEORY Aleksandar Malecic Faculty of Electronic Engineering University of Nis, Serbia [email protected] ABSTRACT In order to identify General Systems Theory (GST) or at least have a fuzzy idea of what it might look like, we shall look for its traces on different systems. We shall try to identify such an “animal” by its “footprints”. First we mention some natural and artificial systems relevant for our search, than note the work of other people within cybernetics and identification of systems, and after that we are focused on what unification of different systems approaches and scientific disciplines should take into account (and whether or not it is possible). Axioms and principles are mentioned as an illustration of how to look for GST*. A related but still separate section is about Len Troncale and linkage propositions. After them there is another overview of different kinds of systems (life, consciousness, and physics). The documentary film Dangerous Knowledge and ideas of its characters Georg Cantor, Ludwig Boltzmann, Kurt Gödel, and Alan Turing are analyzed through systems worldview. “Patterns all the way down” and similar ideas by different authors are elaborated and followed by a section on Daniel Dennett’s approach to real patterns. Two following sections are dedicated to Brian Josephson (a structural theory of everything) and Sunny Auyang. After that the author writes about cosmogony, archetypes, myths, and dogmas. The paper ends with a candidate for GST*. Keywords: General Systems Theory, unification, patterns, principles, linkage propositions SYSTEMS IN NATURE AND ENGINEERING The footprints manifest as phenomena and scientific disciplines.
    [Show full text]
  • Smooth Entropy in Axiomatic Thermodynamics
    Smooth entropy in axiomatic thermodynamics Mirjam Weilenmann1, Lea Kr¨amerGabriel2, Philippe Faist3, and Renato Renner2 1Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK 2Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland 3Institute for Quantum Information and Matter, California Institute of Technology, Pasadena 91125, USA July 23, 2018 Abstract Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including microscopic systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy. 1 Introduction The thermodynamic behaviour of macroscopic systems is traditionally
    [Show full text]
  • A Dynamical Systems Theory of Thermodynamics
    © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. Chapter One Introduction 1.1 An Overview of Classical Thermodynamics Energy is a concept that underlies our understanding of all physical phenomena and is a measure of the ability of a dynamical system to produce changes (motion) in its own system state as well as changes in the system states of its surroundings. Thermodynamics is a physical branch of science that deals with laws governing energy flow from one body to another and energy transformations from one form to another. These energy flow laws are captured by the fundamental principles known as the first and second laws of thermodynamics. The first law of thermodynamics gives a precise formulation of the equivalence between heat (i.e., the transferring of energy via temperature gradients) and work (i.e., the transferring of energy into coherent motion) and states that, among all system transformations, the net system energy is conserved. Hence, energy cannot be created out of nothing and cannot be destroyed; it can merely be transferred from one form to another. The law of conservation of energy is not a mathematical truth, but rather the consequence of an immeasurable culmination of observations over the chronicle of our civilization and is a fundamental axiom of the science of heat. The first law does not tell us whether any particular process can actually occur, that is, it does not restrict the ability to convert work into heat or heat into work, except that energy must be conserved in the process.
    [Show full text]
  • How to Reduce the Second Law of Thermodynamics Katie Robertson
    In Search of the Holy Grail: How to Reduce the Second Law of Thermodynamics Katie Robertson Forthcoming in BJPS 21/4/2020 Abstract The search for the statistical mechanical underpinning of thermodynamic irreversibility has so far focussed on the spontaneous approach to equilibrium. But this is the search for the underpinning of what Brown and Uffink (2001) have dubbed the ‘minus first law’ of thermodynamics. In contrast, the second law tells us that certain interventions on equilibrium states render the initial state ‘irrecoverable’. In this paper, I discuss the unusual nature of processes in thermodynamics, and the type of irreversibility that the second law embodies. I then search for the microscopic underpinning or statistical mechanical ‘reductive basis’ of the second law of thermodynamics by taking a functionalist strategy. First, I outline the functional role of the thermodynamic entropy: for a thermally isolated system, the thermodynamic entropy is constant in quasi-static processes, but increasing in non-quasi-static processes. I then search for the statistical mechanical quantity that plays this role — rather than the role of the traditional ‘holy grail’ as described by Callender (1999). I argue that in statistical mechanics, the Gibbs entropy plays this role. 1 Introduction 2 Functionalism: a tool for reduction 3 The nature of thermodynamic ‘processes’ 3.1 Equilibrium state-space 3.2 Interventions 3.3 Curves: quasi-static processes 3.4 Concepts of Irreversibility 4 The Second Law Introduced 4.1 What type of irreversibility does
    [Show full text]
  • Second Law of Thermodynamics in Non-Extensive Systems
    Second law of thermodynamics in non-extensive systems J.P. Badiali a , A. El Kaabouchi b aUniversit´ePierre et Marie Curie (Paris 6), 4 Place Jussieu, 75230 Paris 05, France bInstitut Sup´erieur des Mat´eriaux et M´ecaniques Avanc´es, 44, Avenue Bartholdi, 72000, Le Mans, France Abstract It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis con- cerning such systems. In the first the existence of an internal coordinate system in which extensivity works is assumed. The second hypothesis concerns the link be- tween this internal coordinate system and the usual thermodynamic variables. This link is represented by an extra relation between two variables pertaining to the two descriptions; to be illustrative a scaling law has been introduced relating external and internal volumes. In addition, we use an axiomatic description based on the ap- proach of the second law of thermodynamics proposed by E. Lieb and J. Yngvason (Physics Reports 310, 1999,1). We show that it exists an entropy function satisfy- ing the monotony of the usual thermodynamic entropy. If a state results from the association of different states, the entropy is additive under these states. However, the entropy is a non-extensive function and we give its law of transformation under a change of the external volume. The entropy is based on some reference states, a change of these states leads to an affine transformation of the entropy. To conclude we can say that the main aspect of the second law of thermodynamics survives in the case of non-extensive systems.
    [Show full text]