View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Apollo Reductive Aspects of Thermal Physics Katie Robertson Pembroke College, University of Cambridge This dissertation is submitted for the degree of Doctor of Philosophy October, 2018 Abstract This thesis examines various reductive case studies in thermal physics. In particular, I argue that according to my account of reduction-as-construction, there are two suc- cessful examples of reduction. Thermodynamics reduces to statistical mechanics, and statistical mechanics reduces to the underlying microdynamics — be they quantum or classical. The reduction of a given theory alters that theory’s scope, that is: its domain of applicability. The scope of thermodynamics will be central to this thesis — and I will argue for a narrower scope than some authors. This thesis consists of four Chapters, together with an introduction and a conclusion. In Chapter 1, I discuss how different levels of description relate to one another. I argue that a higher-level of description is reduced to the lower level, if the higher-level quantities and their behaviour can be constructed or captured by the lower-level theory. I claim that ‘functionalism’ can be helpful in securing reductions. In this Chapter I also argue that the aim of reduction is to vindicate, not eliminate, the higher-level theory. In Chapter 2, I tackle the reduction of thermodynamics to statistical mechanics. I articulate the functional, or nomological, role of various thermodynamic quantities that are implicitly defined by the zeroth, first and second laws of thermodynamics: temperature, energy and entropy respectively. I then argue that there are quantities in statistical mechanics that realise these roles: though finding them sometimes requires us to focus on quantum, rather than classical, statistical mechanics. In Chapter 3, I consider the reductive relationship between statistical mechanics and the underlying microdynamics. I demonstrate how the irreversible equations of statistical mechanics can be constructed from the underlying microdynamics using what I label the ‘Zwanzig-Zeh-Wallace’ framework. Yet this framework uses a procedure called ’coarse-graining’ which has been heavily criticised in the literature; so in this Chapter I offer a justification of coarse-graining. One upshot is that the time-asymmetry in statistical mechanics is weakly emergent. In Chapter 4, I consider a question about the domain of applicability of thermal physics. Namely: does it apply to self-gravitating systems, such as elliptical galaxies? Much controversy surrounds this question: some argue yes, others argue no. I deflate the dispute by claiming that thermodynamics does not apply, but statistical mechanics does. Thus, my delineation of thermodynamics and statistical mechanics earlier in this thesis not only makes headway with the question of reduction, but also sheds light on this dispute. I argue that this situation — statistical mechanics, but without thermodynamics — can be understood in terms of a central notion in thermal physics: the thermodynamic limit. But as I also discuss: justifying this idealisation has been philosophically controversial. 2 Preface This dissertation is the result of my own work and includes nothing which is the out- come of work done in collaboration except as specified in the text. It is not substantially the same as any that I have submitted, or, is being concurrently submitted for a degree or diploma or other qualification at the University of Cambridge or any other Univer- sity or similar institution except as declared in the Preface and specified in the text. I further state that no substantial part of my dissertation has already been submitted, or, is being concurrently submitted for any such degree, diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text. This dissertation does not exceed the word limit of 80,000 words. Chapter 3 is based on a paper forthcoming in the British Journal for the Philosophy of Science. Chapter 4 is based on paper forthcoming in a special issue of Synthese. 3 Acknowledgments Firstly, I would like to thank Jeremy Butterfield for his unstinting generosity with his time, wisdom and patience: not least with my total inability to learn how to use a colon rather than a semi-colon. His guidance and friendship has made the experience of writing a thesis —even when trudging through a bog— truly enjoyable. I owe a large debt of gratitude to many philosophers. Erik Curiel and Owen Maroney have been generous with their time and expertise. I would like to thank Al Wilson for his comments on an earlier draft. For discussion, I would like to thank: Feraz Azhar, Craig Callender, Adam Caulton, Joanna Demaree-Cotton, Natalja Deng, Alex Franklin, Sam Fletcher, Stephan Hartmann, James Ladyman, Casey McCoy, Tushar Menon, Patricia Palacios, Alex Reutlinger, Mathew Simpson, Henry Taylor, David Wallace and Dan Williams. I am grateful to Pembroke College for the support given to me over the last three years, especially through the Hogwood scholarship. I would also like to thank the Munich Centre for Mathematical Philosophy for welcoming me during a research visit in Michaelmas 2017. Here I benefitted from the kind hospitality of the gemütlich Alma Barner and her philosophical insight over a bowl of chocolate muesli. I am very fortunate to have two philosophical friends. Carina Prunkl not only read vast swathes of this thesis, but working together, especially in Munich and Obersdorf, tackling the issues of thermal physics, has always been inspirational. I am deeply grateful to Neil Dewar who has been there every step of the way — reading numerous applications, drafts and listening to my half-baked ideas over a cup of coffee. Without his help and friendship, pursuing philosophy of physics would be a lot less fun. I would also like to thank some non-philosophical friends for their support and encouragement: Charlotte Spires, Grace Edmunds, Louis Devenish, Holly McKenna, Sofia Ropek Hewson, Oliver Burnham and Heather Stallard. Finally, I would like to thank my family — not only for their enduring love and support, but also for helping me finish this thesis: Dad, for proofreading; Mum, for the sandwiches and clothes; my sister Lizzie (MGIF), for always being there; and my partner Joe, for looking after me during the stressful finishing up. But beyond the thesis, my parents (and the organic carrots) have supported and sustained me over many years and given me every possible opportunity, for which I am forever grateful. I dedicate this thesis to them. 4 Contents Introduction 9 1 Wrestling with Reduction 15 1.1 Introduction . 15 1.2 List’s formal framework . 17 1.2.1 Levels of Grain . 18 1.2.2 Levels of Description . 19 1.2.3 Levels of Dynamics . 20 1.2.4 Ontological levels . 22 1.3 Supervenience . 24 1.3.1 The formal idea . 24 1.3.2 The plausibility of supervenience . 25 1.4 Multiple realisability . 27 1.4.1 Multiple realisability: a problem for reduction? . 27 1.4.2 Multiple realisability is widespread — and non-substantive? . 29 1.5 The reduction-as-construction account . 32 1.5.1 Reduction between what? . 33 1.5.2 Reduction-as-construction . 34 1.5.3 Dynamical vs. ‘non-dynamical’ . 36 1.5.4 Two kinds of reduction: vertical and horizontal . 38 1.6 A tool for reduction: Functionalism . 46 1.6.1 Functionalism in the philosophy of physics . 46 1.6.2 Functionalism in the philosophy of mind . 47 1.6.3 Functionalism fit for physics . 49 1.6.4 Conclusion . 52 1.7 Metaphysics and reduction . 52 1.7.1 Emergent special sciences . 54 1.8 Reduction in practice vs in principle . 55 1.9 Conclusion . 57 2 The reduction of thermodynamics to statistical mechanics 75 2.1 Introduction . 75 2.1.1 Silencing scepticism . 76 2.1.2 Autonomy . 77 2.1.3 Prospectus . 79 I. Thermodynamics in general ........................... 80 2.2 Equilibrium state-space . 80 2.3 Dynamics . 81 2.4 Thermodynamics as control theory: Interventions . 85 2.5 Interventions and anthropocentrism . 86 5 Contents 2.6 Statistical mechanics construed . 87 2.6.1 Gibbs vs. Boltzmann . 88 2.6.2 Introducing probability . 89 2.6.3 The Workhorse . 91 2.7 The differing concerns of SM and TD . 93 II. The Zeroth Law .................................. 93 2.8 Pure thermodynamics: the functional role of temperature . 94 2.9 The statistical mechanical realiser . 95 2.10 Batterman’s reconstruction of Gibbs’ objection . 97 2.10.1 The connection to the Canonical Ensemble . 99 2.11 Temperature is not mean kinetic energy . 100 2.11.1 Derivation of the ideal gas law . 100 2.11.2 “T 6= hKi” in general . 102 2.12 Conclusion . 104 III. The First Law ................................... 104 2.13 Phenomenological Statement of the First Law . 105 2.14 A historic achievement . 106 2.15 Done and dusted? . 107 2.16 Molecules in motion . 109 2.16.1 Macro/micro . 109 2.16.2 Anthropocentrism? . 110 2.16.3 More than molecules in motion . 111 2.17 The image in SM: quantum heat and work . 112 2.18 The First Law: Conclusion . 115 IV. The Second Law ................................. 116 2.19 Introduction . 116 2.20 Concepts of Irreversibility . 117 2.21 The source of all asymmetry? . 118 2.22 The Second Law Introduced . 119 2.22.1 Carnot Cycle . 120 2.22.2 Defining Entropy . 121 2.23 Three key features of the TDSL . 123 2.23.1 The importance of the environment . 123 2.23.2 Quasi vs. non-quasi static processes . 124 2.23.3 The Second Law vs. the Minus First Law . 124 2.24 Brownian motion, the Atomic Hypothesis, and the Demonic conse- quences..