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Philosophy of Statistical Mechanics

The Nature of the Past Hypothesis (2016)

To appear in forthcoming volume of proceedings of the conference "Philosophy of Cosmology", Tenerife, 2014.

This is a lightly-edited transcript of my talk at the conference, focussing on the relation between different levels in physics, and in particular between those levels at which the dynamics are time-reversal invariant and those at which they contain irreversibility. We seem to "derive" theories of the latter kind from those of the former kind; what are the assumptions, explicit and tacit, required for us to make sense of these derivations?

Thermodynamics as Control Theory (2013)

Entropy 16.2 (2014) pp. 699-725.

I explore the reduction of thermodynamics to statistical mechanics by treating the former as a control theory: a theory of which transitions between states can be induced on a system (assumed to obey some known underlying dynamics) by means of operations from a fixed list. I recover the results of standard thermodynamics in this framework on the assumption that the available operations do not include measurements which affect subsequent choices of operations. I then relax this assumption and use the framework to consider the vexed questions of Maxwell's demon and Landauer's principle. Throughout I assume rather than prove the basic irreversibility features of statistical mechanics, taking care to distinguish them from the conceptually distinct assumptions of thermodynamics proper.

The Quantitative Content of Statistical Mechanics (2013)

Studies in the History and Philosophy of Modern Physics 52 (2015) pp.285--293.

I give a brief account of the way in which thermodynamics and statistical mechanics actually work as contemporary scientific theories, and in particular of what statistical mechanics contributes to thermodynamics over and above any supposed underpinning of the latter's general principles. In doing so, I attempt to illustrate that statistical mechanics should not be thought of wholly or even primarily as itself a foundational project for thermodynamics, and that conceiving of it this way potentially distorts the foundational study of statistical mechanics itself.

(This paper was originally titled ``What statistical mechanics actually does''; the title was changed at a referee's request.)

Inferential vs. Dynamical Conceptions of Physics (2013)

To appear in What is Quantum Information?, edited by Olympia Lombardi (CUP, forthcoming)

I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations governing particular degrees of freedom). I contrast these attitudes in classical statistical mechanics, in quantum mechanics, and in quantum statistical mechanics; in this last case, I argue that the quantum-mechanical and statistical-mechanical aspects of the question become inseparable. Along the way various foundational issues in statistical and quantum physics are (hopefully!) illuminated.

Recurrence Theorems: a Unified Account (2013)

Journal of Mathematical Physics 65 (2015) 022105.

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces, and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

Probability in Physics: Statistical, Stochastic, Quantum (2013)

In Chance and Temporal Asymmmetry, edited by Alastair Wilson (OUP, 2014)

I review the role of probability in contemporary physics and the origin of probabilistic time asymmetry, beginning with the pre-quantum case (both stochastic mechanics and classical statistical mechanics) but concentrating on quantum theory. I argue that quantum mechanics radically changes the pre-quantum situation and that the philosophical nature of objective probability in physics, and of probabilistic asymmetry in time, is dependent on the correct resolution of the quantum measurement problem.

The Arrow of Time in Physics (2012)

In A Companion to the Philosophy of Time, edited by Adrian Bardon and Heather Dyke (Wiley, 2013)

I provide an overview of the various asymmetries in time --- "Arrows of time" --- found in contemporary physics, predominantly but not exclusively in statistical mechanics and thermodynamics.

The logic of the past hypothesis (2011)

Forthcoming in Time's Arrows and the Probability Structure of the World, edited by Barry Loewer, Eric Winsberg, and Brad Weslake (Harvard, forthcoming)

I attempt to get as clear as possible on the chain of reasoning by which irreversible macrodynamics is derivable from time-reversible microphysics, and in particular to clarify just what kinds of assumptions about the initial state of the universe, and about the nature of the microdynamics, are needed in these derivations. I conclude that while a "Past Hypothesis" about the early Universe does seem necessary to carry out such derivations, that Hypothesis is not correctly understood as a constraint on the early Universe's entropy.

Gravity, Entropy and Cosmology: In Search of Clarity (June 2009)

British Journal for the Philosophy of Science 61 (2010) pp. 513-540

I discuss the statistical mechanics of gravitating systems and in particular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity in entropy calculations must be distinguished from the entropy of gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter itself increases in entropy, and that (iii) the Second Law of Thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse.

Implications of quantum theory in the foundations of statistical mechanics (September 2001)

Online only; cite as

An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time.

(Note: though this has been cited a bit, for various reasons I've never actually got round to publishing it. By now my views have evolved sufficiently that I'm unlikely to publish it without considerable modification.)