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 (...) 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-reversal non-invariance plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. (shrink)

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 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 article, 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. I argue that in statistical mechanics, the Gibbs entropy plays this role. (shrink)

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 (...) focus on two objections in the literature: claims that coarse-graining makes time-asymmetry ‘illusory’ and ‘anthropocentric’. I argue that these objections arise from an unsatisfactory justification of coarse-graining prevalent in the literature, rather than from coarse-graining itself. This justification relies on the idea of measurement imprecision. By considering the role that abstraction and autonomy play, I provide an alternative justification and offer replies to the illusory and anthropocentric objections. Finally, I consider the broader consequences of this alternative justification: the connection to debates about inter-theoretic reduction and the implication that the time-asymmetry in SM is weakly emergent. 1Introduction 1.1Prospectus2The Zwanzig–Zeh–Wallace Framework3Why Does This Method Work? 3.1The special conditions account3.2When is a density forwards-compatible?4Anthropocentrism and Illusion: Two Objections 4.1The two objections in more detail4.2Against the justification by measurement imprecision5An Alternative Justification 5.1Abstraction and autonomy5.2An illustration: the Game of Life6Reply to Illusory7Reply to Anthropocentric8The Wider Landscape: Concluding Remarks 8.1Inter-theoretic relations8.2The nature of irreversibility. (shrink)

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 (...) early universe. This paper aims (i) to distinguish these two different conceptions of the time-asymmetric explanandum in thermodynamics; (ii) to argue in favour of the latter; and (iii) to show that whichever we choose, our rational expectations about the thermodynamic behaviour of the future must depend on what we know about the past: contrary to the common view, statistical arguments alone do not give us good reason to expect that entropy will always continue to increase. (shrink)

A modest proposal concerning laws, counterfactuals, and explanations - - Why be Humean? -- Suggestions from physics for deep metaphysics -- On the passing of time -- Causation, counterfactuals, and the third factor -- The whole ball of wax -- Epilogue : a remark on the method of metaphysics.

This essay explains what the Causal Markov Condition says and defends the condition from the many criticisms that have been launched against it. Although we are skeptical about some of the applications of the Causal Markov Condition, we argue that it is implicit in the view that causes can be used to manipulate their effects and that it cannot be surrendered without surrendering this view of causation.

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 (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

“The universe is expanding, not contracting.” Many statements of this form appear unambiguously true; after all, the discovery of the universe’s expansion is one of the great triumphs of empirical science. However, the statement is time-directed: the universe expands towards what we call the future; it contracts towards the past. If we deny that time has a direction, should we also deny that the universe is really expanding? This article draws together and discusses what I call ‘C-theories’ of time — (...) in short, philosophical positions that hold time lacks a direction — from different areas of the literature. I set out the various motivations, aims, and problems for C-theories, and outline different versions of antirealism about the direction of time. (shrink)

In what sense is the direction of time a matter of convention? In 'The Direction of Time', Hans Reichenbach makes brief reference to parallels between his views about the status of time’s direction and his conventionalism about geometry. In this article, I: (1) provide a conventionalist account of time direction motivated by a number of Reichenbach’s claims in the book; (2) show how forwards and backwards time can give equivalent descriptions of the world despite the former being the ‘natural’ direction (...) of time; and (3) argue that this offers an important middle-ground position between existing realist and antirealist accounts of the direction of time. (shrink)

For the generalizations of thermodynamics to obtain, it appears that a very ‘special’ initial condition of the universe is required. Is this initial condition itself in need of explanation? I argue that it is not. In so doing, I offer a framework in which to think about ‘special’ initial conditions in all areas of science, though I concentrate on the case of thermodynamics. I urge the view that it is not always a serious mark against a theory that it must (...) posit an ‘improbable’ initial condition. (shrink)

Philosophers of physics have long debated whether the Past State of low entropy of our universe calls for explanation. What is meant by “calls for explanation”? In this article we analyze this notion, distinguishing between several possible meanings that may be attached to it. Taking the debate around the Past State as a case study, we show how our analysis of what “calling for explanation” might mean can contribute to clarifying the debate and perhaps to settling it, thus demonstrating the (...) fruitfulness of this analysis. Applying our analysis, we show that two main opponents in this debate, Huw Price and Craig Callender, are, for the most part, talking past each other rather than disagreeing, as they employ different notions of “calling for explanation”. We then proceed to show how answering the different questions that arise out of the different meanings of “calling for explanation” can result in clarifying the problems at hand and thus, hopefully, to solving them. (shrink)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the ...

This is an extensive review of recent work on the foundations of statistical mechanics.

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. (shrink)

Modern physics has provided a range of motivations for holding time to be fundamentally undirected. But how does a temporally adirectional metaphysics, or ‘C-theory’ of time, fit with the time of experience? In this chapter, I look at what kind of problem human time poses for C-theories. First, I ask whether there is a ‘hard problem’ of human time: whether it is in principle impossible to have the kinds of experience we do in a temporally adirectional world. Second I consider (...) the ‘easy problem’: how specific directed aspects of our temporal experience are to be explained by C-theorists. This leads to a greater issue: is there such a thing as an experience of time direction at all to even be explained? I show how the kinds of experience we have that we typically associate with the idea of time being directed can be accommodated within a directionless picture of time. (shrink)

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very notion (...) of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)

Suppose that God or a demon informs you of the following future fact: despite recent cosmological evidence, the universe is indeed closed and it will have a ‘final’ instant of time; moreover, at that final moment, all 49 of the world’s Imperial Faberge eggs will be in your bedroom bureau’s sock drawer. You’re absolutely certain that this information is true. All of your other dealings with supernatural powers have demonstrated that they are a trustworthy lot.

Are principles of information processing necessary to demonstrate the consistency of statistical mechanics? Does the physical implementation of a computational operation have a fundamental thermodynamic cost, purely by virtue of its logical properties? These two questions lie at the centre of a large body of literature concerned with the Szilard engine (a variant of the Maxwell's demon thought experiment), Landauer's principle (supposed to embody the fundamental principle of the thermodynamics of computation) and possible connections between the two. A variety of (...) attempts to answer these questions have illustrated many open questions in the foundations of statistical mechanics. (shrink)

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 (...) supposed conceptual problems with the Gibbsian approach are either misconceived, or apply only to certain versions of the Gibbsian approach, or apply with equal force to both approaches. I conclude that Boltzmannian statistical mechanics is best seen as a special case of, and not an alternatve to, Gibbsian statistical mechanics. (shrink)

Let us begin with a characteristic example. Consider a gas that is confined to the left half of a box. Now we remove the barrier separating the two halves of the box. As a result, the gas quickly disperses, and it continues to do so until it homogeneously fills the entire box. This is illustrated in Figure 1.