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  1. Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State.Eddy Keming Chen - 2021 - British Journal for the Philosophy of Science 72 (4):1155–1183.
    In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave Function (...)
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  • The logic of the past hypothesis.David Wallace - 2023 - In Barry Loewer, Brad Weslake & Eric B. Winsberg (eds.), The Probability Map of the Universe: Essays on David Albert’s _Time and Chance_. Cambridge MA: Harvard University Press. pp. 76-109.
    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 (...)
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  • Who’s Afraid of Nagelian Reduction?Foad Dizadji-Bahmani, Roman Frigg & Stephan Hartmann - 2010 - Erkenntnis 73 (3):393-412.
    We reconsider the Nagelian theory of reduction and argue that, contrary to a widely held view, it is the right analysis of intertheoretic reduction. The alleged difficulties of the theory either vanish upon closer inspection or turn out to be substantive philosophical questions rather than knock-down arguments.
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  • Nomothetic Explanation and Humeanism about Laws of Nature.Harjit Bhogal - 2020 - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics Volume 12. Oxford University Press. pp. 164–202.
    Humeanism about laws of nature — the view that the laws reduce to the Humean mosaic — is a popular view, but currently existing versions face powerful objections. The non-supervenience objection, the non-fundamentality objection and the explanatory circularity objection have all been thought to cause problems for the Humean. However, these objections share a guiding thought — they are all based on the idea that there is a certain kind of divergence between the practice of science and the metaphysical picture (...)
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  • Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities.Eddy Keming Chen - 2020 - In Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature. Singapore: World Scientific. pp. 479–515.
    In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...)
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  • Quantum states for primitive ontologists: A case study.Gordon Belot - 2012 - European Journal for Philosophy of Science 2 (1):67-83.
    Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...)
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  • Fitness, probability and the principles of natural selection.Frederic Bouchard & Alexander Rosenberg - 2004 - British Journal for the Philosophy of Science 55 (4):693-712.
    We argue that a fashionable interpretation of the theory of natural selection as a claim exclusively about populations is mistaken. The interpretation rests on adopting an analysis of fitness as a probabilistic propensity which cannot be substantiated, draws parallels with thermodynamics which are without foundations, and fails to do justice to the fundamental distinction between drift and selection. This distinction requires a notion of fitness as a pairwise comparison between individuals taken two at a time, and so vitiates the interpretation (...)
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  • Bluff Your Way in the Second Law of Thermodynamics.Jos Uffink - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (3):305-394.
    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-reversal (non-)invariance 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 (...)
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  • Statistical Mechanics and the Asymmetry of Counterfactual Dependence.Adam Elga - 2000 - Philosophy of Science 68 (3):313-324.
    In "Counterfactual Dependence and Time's Arrow", David Lewis defends an analysis of counterfactuals intended to yield the asymmetry of counterfactual dependence: that later affairs depend counterfactually on earlier ones, and not the other way around. I argue that careful attention to the dynamical properties of thermodynamically irreversible processes shows that in many ordinary cases, Lewis's analysis fails to yield this asymmetry. Furthermore, the analysis fails in an instructive way: it teaches us something about the connection between the asymmetry of overdetermination (...)
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  • Emergence, Singularities, and Symmetry Breaking.Robert W. Batterman - 2011 - Foundations of Physics 41 (6):1031-1050.
    This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.
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  • Critical phenomena and breaking drops: Infinite idealizations in physics.Robert Batterman - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2):225-244.
    Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to mistakes in Statistical Mechanics. I discuss (...)
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  • The Oxford Handbook of Philosophical Methodology.Herman Cappelen, Tamar Gendler & John Hawthorne (eds.) - 2016 - Oxford, United Kingdom: Oxford University Press.
    This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...)
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  • Entropy - A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford, GB: Oxford University Press. pp. 115-142.
    Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...)
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  • Asymmetry, Abstraction, and Autonomy: Justifying Coarse-Graining in Statistical Mechanics.Katie Robertson - 2020 - British Journal for the Philosophy of Science 71 (2):547-579.
    While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics, progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced much criticism. I (...)
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  • Justifying definitions in mathematics—going beyond Lakatos.Charlotte Werndl - 2009 - Philosophia Mathematica 17 (3):313-340.
    This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in ergodic theory, I identify three other common ways of justifying definitions: natural-world justification, condition justification, and redundancy justification. Also, I clarify the interrelationships between the different kinds of justification. Finally, I point out how Lakatos's ideas are limited: they fail to show how various kinds of justification (...)
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  • Typicality and the approach to equilibrium in Boltzmannian statistical mechanics.Roman Frigg - 2009 - Philosophy of Science 76 (5):997-1008.
    An important contemporary version of Boltzmannian statistical mechanics explains the approach to equilibrium in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognized as such and not clearly distinguished. This article identifies three different versions of typicality‐based explanations of thermodynamic‐like behavior and evaluates their respective successes. The conclusion is that the first two are unsuccessful because they fail to take the system's dynamics into account. The third, however, is promising. (...)
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  • Deidealization: No Easy Reversals.Tarja Knuuttila & Mary S. Morgan - 2019 - Philosophy of Science 86 (4):641-661.
    Deidealization as a topic in its own right has attracted remarkably little philosophical interest despite the extensive literature on idealization. One reason for this is the often implicit assumption that idealization and deidealization are, potentially at least, reversible processes. We question this assumption by analyzing the challenges of deidealization within a menu of four broad categories: deidealizing as recomposing, deidealizing as reformulating, deidealizing as concretizing, and deidealizing as situating. On closer inspection, models turn out much more inflexible than the reversal (...)
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  • Can conditioning on the “past hypothesis” militate against the reversibility objections?Eric Winsberg - 2004 - Philosophy of Science 71 (4):489-504.
    In his recent book, Time and Chance, David Albert claims that by positing that there is a uniform probability distribution defined, on the standard measure, over the space of microscopic states that are compatible with both the current macrocondition of the world, and with what he calls the “past hypothesis”, we can explain the time asymmetry of all of the thermodynamic behavior in the world. The principal purpose of this paper is to dispute this claim. I argue that Albert's proposal (...)
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  • Statistics, Symmetry, and the Conventionality of Indistinguishability in Quantum Mechanics.Darrin W. Belousek - 2000 - Foundations of Physics 30 (1):1-34.
    The question to be addressed is, In what sense and to what extent do quantum statistics for, and the standard formal quantum-mechanical description of, systems of many identical particles entail that identical quantum particles are indistinguishable? This paper argues that whether or not we consider identical quantum particles as indistinguishable is a matter of theory choice underdetermined by logic and experiment.
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  • Special Sciences, Conspiracy and the Better Best System Account of Lawhood.Jonathan Cohen & Craig Callender - 2010 - Erkenntnis 73 (3):427 - 447.
    An important obstacle to lawhood in the special sciences is the worry that such laws would require metaphysically extravagant conspiracies among fundamental particles. How, short of conspiracy, is this possible? In this paper we'll review a number of strategies that allow for the projectibility of special science generalizations without positing outlandish conspiracies: non-Humean pluralism, classical MRL theories of laws, and Albert and Loewer's theory. After arguing that none of the above fully succeed, we consider the conspiracy problem through the lens (...)
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  • Explaining Thermodynamic-Like Behavior in Terms of Epsilon-Ergodicity.Roman Frigg & Charlotte Werndl - 2011 - Philosophy of Science 78 (4):628-652.
    Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...)
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  • Thermodynamic asymmetry in time.Craig Callender - 2006 - Stanford Encyclopedia of Philosophy.
    Thermodynamics is the science that describes much of the time asymmetric behavior found in the world. This entry's first task, consequently, is to show how thermodynamics treats temporally ‘directed’ behavior. It then concentrates on the following two questions. (1) What is the origin of the thermodynamic asymmetry in time? In a world possibly governed by time symmetric laws, how should we understand the time asymmetric laws of thermodynamics? (2) Does the thermodynamic time asymmetry explain the other temporal asymmetries? Does it (...)
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  • Minkowski spacetime and Lorentz invariance: The cart and the horse or two sides of a single coin.Pablo Acuña - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 55:1-12.
    Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation (...)
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  • Chance, Possibility, and Explanation.Nina Emery - 2015 - British Journal for the Philosophy of Science 66 (1):95-120.
    I argue against the common and influential view that non-trivial chances arise only when the fundamental laws are indeterministic. The problem with this view, I claim, is not that it conflicts with some antecedently plausible metaphysics of chance or that it fails to capture our everyday use of ‘chance’ and related terms, but rather that it is unstable. Any reason for adopting the position that non-trivial chances arise only when the fundamental laws are indeterministic is also a reason for adopting (...)
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  • Two Approaches to Reduction: A Case Study from Statistical Mechanics.Bixin Guo - forthcoming - Philosophy of Science:1-36.
    I argue that there are two distinct approaches to understanding reduction: the ontology-first approach and the theory-first approach. They concern the relation between ontological reduction and inter-theoretic reduction. Further, I argue for the significance of this distinction by demonstrating that either one or the other approach has been taken as an implicit assumption in, and has in fact shaped, our understanding of what statistical mechanics is. More specifically, I argue that the Boltzmannian framework of statistical mechanics assumes and relies on (...)
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  • Statistical Mechanics: A Tale of Two Theories.Roman Frigg & Charlotte Werndl - 2019 - The Monist 102 (4):424-438.
    There are two theoretical approaches in statistical mechanics, one associated with Boltzmann and the other with Gibbs. The theoretical apparatus of the two approaches offer distinct descriptions of the same physical system with no obvious way to translate the concepts of one formalism into those of the other. This raises the question of the status of one approach vis-à-vis the other. We answer this question by arguing that the Boltzmannian approach is a fundamental theory while Gibbsian statistical mechanics is an (...)
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  • Boltzmann’s Time Bomb.Huw Price - 2002 - British Journal for the Philosophy of Science 53 (1):83-119.
    Since the late nineteenth century, physics has been puzzled by the time-asymmetry of thermodynamic phenomena in the light of the apparent T-symmetry of the underlying laws of mechanics. However, a compelling solution to this puzzle has proved elusive. In part, I argue, this can be attributed to a failure to distinguish two conceptions of the problem. According to one, the main focus of our attention is a time-asymmetric lawlike generalisation. According to the other, it is a particular fact about the (...)
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  • The Necessity of Gibbsian Statistical Mechanics.David Wallace - unknown
    In discussions of the foundations of statistical mechanics, it is widely held that the Gibbsian and Boltzmannian approaches are incompatible but empirically equivalent; the Gibbsian approach may be calculationally preferable but only the Boltzmannian approach is conceptually satisfactory. I argue against both assumptions. Gibbsian statistical mechanics is applicable to a wide variety of problems and systems, such as the calculation of transport coefficients and the statistical mechanics and thermodynamics of mesoscopic systems, in which the Boltzmannian approach is inapplicable. And the (...)
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  • Mechanistic probability.Marshall Abrams - 2012 - Synthese 187 (2):343-375.
    I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it's a virtue rather than (...)
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  • (1 other version)Boltzmann's H-theorem, its discontents, and the birth of statistical mechanics.Harvey R. Brown, Wayne Myrvold & Jos Uffink - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (2):174-191.
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  • What’s so special about initial conditions? Understanding the past hypothesis in directionless time.Matt Farr - 2022 - In Yemima Ben-Menahem (ed.), Rethinking Laws of Nature. Springer.
    It is often said that the world is explained by laws of nature together with initial conditions. But does that mean initial conditions don’t require further explanation? And does the explanatory role played by initial conditions entail or require that time has a preferred direction? This chapter looks at the use of the ‘initialness defence’ in physics, the idea that initial conditions are intrinsically special in that they don’t require further explanation, unlike the state of the world at other times. (...)
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  • The Arrow of Time in Physics.David Wallace - 2013 - In Adrian Bardon & Heather Dyke (eds.), A Companion to the Philosophy of Time. Malden, MA: Wiley-Blackwell. pp. 262–281.
    Every process studied in any science other than physics defines an arrow of time – to say nothing for the directedness of the processes of causation, inference, memory, control, and counterfactual dependence that occur in everyday life. The discussion in this chapter is confined to the arrow of time as it occurs in physics. The chapter briefly discusses those features of microscopic physics, which seem to conflict with time asymmetry. It explains just how this conflict plays out in the important (...)
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  • Causation, physics, and fit.Christian Loew - 2017 - Synthese 194 (6):1945–1965.
    Our ordinary causal concept seems to fit poorly with how our best physics describes the world. We think of causation as a time-asymmetric dependence relation between relatively local events. Yet fundamental physics describes the world in terms of dynamical laws that are, possible small exceptions aside, time symmetric and that relate global time slices. My goal in this paper is to show why we are successful at using local, time-asymmetric models in causal explanations despite this apparent mismatch with fundamental physics. (...)
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  • The emergence of macroscopic regularity.Meir Hemmo & Orly Shenker - 2015 - Mind and Society 14 (2):221-244.
    Special sciences (such as biology, psychology, economics) describe various regularities holding at some high macroscopic level. One of the central questions concerning these macroscopic regularities is how they are related to the laws of physics governing the underlying microscopic physical reality. In this paper we show how a macroscopic regularity may emerge from an underlying micro- scopic structure, and how the appearance of multiple realizability of the special sciences by physics comes about in a reductionist-physicalist framework. On this basis we (...)
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  • Reduction, integration, and the unity of science: Natural, behavioral, and social sciences and the humanities.William P. Bechtel & Andrew Hamilton - 2007 - In T. Kuipers (ed.), Philosophy of Science: Focal Issues (Volume 1 of the Handbook of the Philosophy of Science). Elsevier.
    1. A Historical Look at Unity 2. Field Guide to Modern Concepts of Reduction and Unity 3. Kitcher's Revisionist Account of Unification 4. Critics of Unity 5. Integration Instead of Unity 6. Reduction via Mechanisms 7. Case Studies in Reduction and Unification across the Disciplines.
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  • An empirical approach to symmetry and probability.Jill North - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):27-40.
    We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...)
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  • (1 other version)The emergence and interpretation of probability in Bohmian mechanics.Craig Callender - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):351-370.
    A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born’s rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging (...)
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  • Chance versus Randomness.Antony Eagle - 2010 - Stanford Encyclopedia of Philosophy.
    This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic relatively unfamiliar to philosophers.
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  • (1 other version)Contemporary debates in philosophy of science.Christopher Hitchcock (ed.) - 2004 - Malden, MA: Blackwell.
    Showcasing original arguments for well-defined positions, as well as clear and concise statements of sophisticated philosophical views, this volume is an ...
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  • Implications of quantum theory in the foundations of statistical mechanics.David Wallace - manuscript
    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 (...)
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  • The global non-entropic arrow of time: from global geometrical asymmetry to local energy flow.Mario Castagnino & Olimpia Lombardi - 2009 - Synthese 169 (1):1-25.
    Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the global non-entropic arrow can (...)
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  • The Direction of Time.Steven F. Savitt - 1996 - British Journal for the Philosophy of Science 47 (3):347-370.
    The aim of this essay is to introduce philosophers of science to some recent philosophical discussions of the nature and origin of the direction of time. The essay is organized around books by Hans Reichenbach, Paul Horwich, and Huw Price. I outline their major arguments and treat certain critical points in detail. I speculate at the end about the ways in which the subject may continue to develop and in which it may connect with other areas of philosophy.
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  • On the neglect of the philosophy of chemistry.J. van Brakel - 1999 - Foundations of Chemistry 1 (2):111-174.
    In this paper I present a historiography of the recent emergence of philosophy of chemistry. Special attention is given to the interest in this domain in Eastern Europe before the collapse of the USSR. It is shown that the initial neglect of the philosophy of chemistry is due to the unanimous view in philosophy and philosophy of science that only physics is a proper science (to put in Kant's words). More recently, due to the common though incorrect assumption that chemistry (...)
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  • (1 other version)Why typicality does not explain the approach to equilibrium.Roman Frigg - 2011 - In .
    Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations (...)
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  • Autonomy generalised; or, Why doesn’t physics matter more?Katie Robertson - forthcoming - Ergo.
    In what sense are the special sciences autonomous of fundamental physics? Autonomy is an enduring theme in discussions of the relationship between the special sciences and fundamental physics or, more generally, between higher and lower-level facts. Discussion of ‘autonomy’ often fails to recognise that autonomy admits of degrees; consequently, autonomy is either taken to require full independence, or risk relegation to mere apparent autonomy. In addition, the definition of autonomy used by Fodor, the most famous proponent of the autonomy of (...)
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  • The ergodic hierarchy.Roman Frigg & Joseph Berkovitz - 2011 - Stanford Encyclopedia of Philosophy.
    The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.
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  • Probability in Boltzmannian statistical mechanics.Roman Frigg - 2010 - In Gerhard Ernst & Andreas Hüttemann (eds.), Time, chance and reduction: philosophical aspects of statistical mechanics. New York: Cambridge University Press.
    In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as Humean chances in David Lewis’ (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically.
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  • Contemporary Approaches to Statistical Mechanical Probabilities: A Critical Commentary - Part I: The Indifference Approach.Christopher J. G. Meacham - 2010 - Philosophy Compass 5 (12):1116-1126.
    This pair of articles provides a critical commentary on contemporary approaches to statistical mechanical probabilities. These articles focus on the two ways of understanding these probabilities that have received the most attention in the recent literature: the epistemic indifference approach, and the Lewis-style regularity approach. These articles describe these approaches, highlight the main points of contention, and make some attempts to advance the discussion. The first of these articles provides a brief sketch of statistical mechanics, and discusses the indifference approach (...)
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  • Can Informational Thermal Physics explain the Approach to Equilibrium?Javier Anta - 2021 - Synthese 199 (1-2):4015–4038.
    In this paper I will defend the incapacity of the informational frameworks in thermal physics, mainly those that historically and conceptually derive from the work of Brillouin (1962) and Jaynes (1957a), to robustly explain the approach of certain gaseous systems to their state of thermal equilibrium from the dynamics of their molecular components. I will further argue that, since their various interpretative, conceptual and technical-formal resources (e.g. epistemic interpretations of probabilities and entropy measures, identification of thermal entropy as Shannon information, (...)
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  • Typicality and the role of the Lebesgue measure in statistical mechanics.Itamar Pitowsky - 2012 - In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. pp. 41--58.
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