In (Weaver 2021), I showed that Boltzmann’s H-theorem does not face a significant threat from the reversibility paradox. I argue that my defense of the H-theorem against that paradox can be used yet again for the purposes of resolving the recurrence paradox without having to endorse heavy-duty statistical assumptions outside of the hypothesis of molecular chaos. As in (Weaver 2021), lessons from the history and foundations of physics reveal precisely how such resolution is achieved.

The main objective of this dissertation is to philosophically assess how the use of informational concepts in the field of classical thermostatistical physics has historically evolved from the late 1940s to the present day. I will first analyze in depth the main notions that form the conceptual basis on which 'informational physics' historically unfolded, encompassing (i) different entropy, probability and information notions, (ii) their multiple interpretative variations, and (iii) the formal, numerical and semantic-interpretative relationships among them. In the following, I (...) will assess the history of informational thermophysics during the second half of the twentieth century. Firstly, I analyse the intellectual factors that gave rise to this current in the late forties (i.e., popularization of Shannon's theory, interest in a naturalized epistemology of science, etc.), then study its consolidation in the Brillouinian and Jaynesian programs, and finally claim how Carnap (1977) and his disciples tried to criticize this tendency within the scientific community. Then, I evaluate how informational physics became a predominant intellectual current in the scientific community in the nineties, made possible by the convergence of Jaynesianism and Brillouinism in proposals such as that of Tribus and McIrvine (1971) or Bekenstein (1973) and the application of algorithmic information theory into the thermophysical domain. As a sign of its radicality at this historical stage, I explore the main proposals to include information as part of our physical reality, such as Wheeler’s (1990), Stonier’s (1990) or Landauer’s (1991), detailing the main philosophical arguments (e.g., Timpson, 2013; Lombardi et al. 2016a) against those inflationary attitudes towards information. Following this historical assessment, I systematically analyze whether the descriptive exploitation of informational concepts has historically contributed to providing us with knowledge of thermophysical reality via (i) explaining thermal processes such as equilibrium approximation, (ii) advantageously predicting thermal phenomena, or (iii) enabling understanding of thermal property such as thermodynamic entropy. I argue that these epistemic shortcomings would make it impossible to draw ontological conclusions in a justified way about the physical nature of information. In conclusion, I will argue that the historical exploitation of informational concepts has not contributed significantly to the epistemic progress of thermophysics. This would lead to characterize informational proposals as 'degenerate science' (à la Lakatos 1978a) regarding classical thermostatistical physics or as theoretically underdeveloped regarding the study of the cognitive dynamics of scientists in this physical domain. (shrink)

The thesis proposes, defends, and applies a new model of inter-theoretic reduction, called "Neo-Nagelian" reduction. There are numerous accounts of inter-theoretic reduction in the philosophy of science literature but the most well-known and widely-discussed is the Nagelian one. In the thesis I identify various kinds of problems which the Nagelian model faces. Whilst some of these can be resolved, pressing ones remain. In lieu of the Nagelian model, other models of inter-theoretic reduction have been proposed, chief amongst which are so-called (...) "New Wave" models. I show these to be no more adequate than the original Nagelian model. I propose a new model of inter-theoretic reduction, Neo-Nagelian reduction. This model is structurally similar to the Nagelian one, but differs in substantive ways. In particular I argue that it avoids the problems pertaining to both the Nagelian and New Wave models. Multiple realizability looms large in discussions about reduction: it is claimed that multiply realizable properties frustrate the reduction of one theory to another in various ways. I consider these arguments and show that they do not undermine the Neo-Nagelian of reduction of one theory to another. Finally, I apply the model to statistical mechanics. Statistical mechanics is taken to be a reductionist enterprise: one of the aims of statistical mechanics is to reduce thermodynamics. Without an adequate model of inter-theoretic reduction one cannot assess whether it succeeds; I use the Neo-Nagelian model to critically discuss whether it does. Specifically, I consider two very recent derivations of the Second Law of thermodynamics, one from Boltzmannian classical statistical mechanics and another from quantum statistical mechanics. I argue that they are partially successful, and that each makes for a promising line of future research. (shrink)

Landauer’s principle is, roughly, the principle that logically irreversible operations cannot be performed without dissipation of energy, with a specified lower bound on that dissipation. Although widely accepted in the literature on the thermodynamics of computation, it has been the subject of considerable dispute in the philosophical literature. Proofs of the principle have been questioned on the grounds of insufficient generality and on the grounds of the assumption, used in the proofs, of the availability of reversible processes at the microscale. (...) The relevance of the principle, should it be true, has also been questioned, as it has been argued that microscale fluctuations entail dissipation that always greatly exceeds the Landauer bound. In this article Landauer’s principle is treated within statistical mechanics, and a proof of the principle is given that neither relies on neglect of fluctuations nor assumes the availability of thermodynamically reversible processes. In addition, it is argued that microscale fluctuations are no obstacle to approximating thermodynamic reversibility, in the appropriate sense, as closely as one would like. (shrink)

In this paper I will evaluate whether some knowledge states that are interpretatively derived from statistical mechanical probabilities could be somehow relevant in actual practices, as famously rejected by Albert (2000). On one side, I follow Frigg (2010a) in rejecting the causal relevance of knowledge states as a mere byproduct of misinterpreting this theoretical field. On the other side, I will argue against Uffink (2011) that probability-represented epistemic states cannot be explanatorily relevant, because (i) probabilities cannot faithfully represent significant epistemic (...) states, and (ii) those states cannot satisfactorily account for why an agent should theoretically believe or expect something. (shrink)

I will argue, pace a great many of my contemporaries, that there's something right about Boltzmann's attempt to ground the second law of thermodynamics in a suitably amended deterministic time-reversal invariant classical dynamics, and that in order to appreciate what's right about (what was at least at one time) Boltzmann's explanatory project, one has to fully apprehend the nature of microphysical causal structure, time-reversal invariance, and the relationship between Boltzmann entropy and the work of Rudolf Clausius.

There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics, but as a theory of how manipulations of a physical system may be used to obtain desired effects, such as mechanical work. On this view, the basic concepts of thermodynamics, heat and work, and with them, the concept of entropy, are relative to a class of envisaged manipulations. This article is a sketch and defense of a science of manipulations and their effects on physical (...) systems. I call this science thermo-dynamics, or ΘΔcs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta \Delta }^{\text{cs}}$$\end{document}, for short, to highlight that it may be different from the science of thermodynamics, as the reader conceives it. An upshot of the discussion is a clarification of the roles of the Gibbs and von Neumann entropies. Light is also shed on the use of coarse-grained entropies. (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)

The mind of man is central to the structure and functioning of the physical world. Modern physical theory indicates that the mind stands in a relationship of equals to the physical world. Both are fundamental, neither can be reduced to the other, and both require each other for their full understanding. This thesis is at odds with the view of the universe found in Newtonian mechanics as well as the generally held view among contemporary physicists of modern physical theory. Since (...) the Renaissance, man has come to understand a great deal about the physical world, and he has gained significant control over it. This increased power over the physical world has occurred hand in hand with the assumption that the structure and functioning of the physical world is essentially independent from his cognitive functioning. According to this assumption, if man’s cognitive capacity did not exist, the functioning of the physical world would not be fundamentally altered. This last statement is not in fact correct, and modern physical theory, and even fundamentals underlying Newtonian mechanics, provide evidence to attest to this. Nonetheless, contemporary physicists for the most part do not see that the relationship of human cognition to the physical world is radically altered in their own modern theory, theory that is supported by a great deal of empirical data. Instead, attempting to preserve the thesis that the structure and functioning of the physical world is independent of the mind while on a practical level relying on modern theory that contradicts this thesis, physicists have placed themselves in the position of wondering at times exactly what is the nature of the physical world at the same time they obtain experimental results concerning the physical world that can only be labeled astonishing in their precision and the scope of their implications. Modern physical theory consists of three main components: 1) the special and general theories of relativity; 2) quantum mechanics; and 3) statistical mechanics. There are very successful theories that have been developed on the basis of these three bedrock areas. An example of one is quantum electrodynamics. But these theories owe their conceptual foundation to the three components mentioned. The basic issues at the core of these three components also are expressed in these later theories. In addition, there are new unresolved issues of a fundamental nature concerning the conceptual integrity of these later theories that do not apply to quantum mechanics, relativity theory, and statistical mechanics. Quantum mechanics and relativity theory are areas I have written about for over twelve years. The nature of statistical mechanics has also been of interest to me during this time. But when I took a serious look in 1993 at Tolman’s (1938) The Principles of Statistical Mechanics, it became clear that the mind is linked to the physical world in statistical mechanics, a relationship I had found earlier in both relativity theory and quantum mechanics. It was after reading Tolman’s justification of the method of statistical mechanics in the original that I decided to write this book. When I found that the three components of modern physical theory all pointed to the same relationship between mind and the physical world, it became clear that the fundamental isolation of the mind from the physical world that has characterized our experience since the development of Newtonian mechanics is unfounded. Based on empirically supported principles of modern physical theory, I determined that the appropriate assumption for one’s experience, that the mind is linked to the physical world, could be stated with confidence. The impact of this change in assumption concerning the relationship of man to the cosmos in modern physical theory will find its way into our everyday experience. It will perhaps have no greater effect than in reducing the sense of isolation of man from the world that has characterized modern existence. (shrink)

The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides general (...) criteria for the existence of an equilibrium state. We first illustrate how the theorem works with a toy example, which allows us to illustrate the various elements of the theorem in a simple setting. After a look at the ergodic programme, we discuss equilibria in a number of different gas systems: the ideal gas, the dilute gas, the Kac gas, the stadium gas, the mushroom gas and the multi-mushroom gas. In the conclusion we briefly summarise the main points and highlight open questions. (shrink)

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 (...) the pros and cons of various positions, it defends particular answers to how the probabilities emerge from Bohmian mechanics and how they ought to be interpreted. (shrink)

I contrast two possible attitudes towards a given branch of physics: as inferential, and as dynamical. 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 illuminated.

One popular approach to statistical mechanics understands statistical mechanical probabilities as measures of rational indifference. Naive formulations of this ``indifference approach'' face reversibility worries - while they yield the right prescriptions regarding future events, they yield the wrong prescriptions regarding past events. This paper begins by showing how the indifference approach can overcome the standard reversibility worries by appealing to the Past Hypothesis. But, the paper argues, positing a Past Hypothesis doesn't free the indifference approach from all reversibility worries. For (...) while appealing to the Past Hypothesis allows it to escape one kind of reversibility worry, it makes it susceptible to another - the Meta-Reversibility Objection. And there is no easy way for the indifference approach to escape the Meta-Reversibility Objection. As a result, reversibility worries pose a steep challenge to the viability of the indifference approach. (shrink)

This project is about the asymmetry of time. The main source of discontent for physicists and philosophers alike is that even though in every physical theory we developed and/or discovered for explaining how the universe functions, the laws are time reversal invariant; there seems to be a very genuine asymmetry between the past and the future. The aim of this project is to examine several attempts to solve this friction between the laws of physics and the asymmetry and provide a (...) new proposal that makes use of modern cosmology. In the recent history of physics and in contemporary philosophy of science there have been several attempts to explain the asymmetry of time and reconcile this asymmetry with time reversal invariant physical laws. David Albert developed one of the most recent attempts at solving the problem in Time and Chance (2000). Albert claims that there is a conclusive solution to the problem of asymmetry of time: namely, combining the laws of mechanics with several novel concepts that he introduces, the most important of which is what he calls "the past hypothesis". Eric Winsberg developed another modern attempt to solve the problem of the asymmetry of time. Winsberg combines Hans Reichenbach's branch systems proposal with a "framework" view of laws to solve the problem. Although this version of the branch systems proposal overcomes several problems associated with Reichenbach's original construction of the proposal, certain aspects of it are still open to critique. Following a brief introduction, my chapters include 1) a history of the problem of the asymmetry of time, in which I provide a historical overview of the issues particularly discussed by Boltzmann and his interlocutors, 2) a detailed evaluation of David Albert's account of the asymmetry of time, where he argues that we can solve all the problems if we use a combination of laws of physics and the past hypothesis, 3) a detailed overview of Eric Winsberg's account that depends a specific way of looking at the laws of physics--the framework view, and 4) my account, which attempts to solve the problem of the asymmetry of time, making extensive use of the developments on modern cosmology, specifically regarding the inflationary mechanism. I claim that if we take into account recent developments in modern cosmology and proposals for laws for initial conditions, then we cannot maintain the metaphysical status of the past hypothesis in Albert's project. Specifically, I argue that in order for a theory to make use of initial conditions of the universe, it has to include a set of laws from modern cosmology pertaining to that initial condition. I defend the position that inflation can supply the source of asymmetry when supported by the aggregate view of laws, which I introduce in the last chapter. The explanation of the asymmetry of time requires the use of dynamical equations from modern cosmology that would produce the boundary conditions. The boundary condition produced in this way would fill in for the source of the asymmetry of time. Consequently, I argue that the explanation of the asymmetry of time is encoded in the laws of modern cosmology. (shrink)

Simple models have played an important role in the discussion of foundational issues in statistical mechanics. Among them the spin-echo system is of particular interest since it can be realized experimentally. This has led to inferences being drawn about approaches to the foundations of statistical mechanics, particularly with respect to the use of coarse-graining. We examine these claims with the help of computer simulations.

Bose-Einstein statistics may be characterized in terms of multinomial distribution. From this characterization, an information theoretic analysis is made for Einstein-Podolsky-Rosen like situation; using Shannon’s measure of entropy.

The meaning of the phrase “the direction of time” and the physical problems involved are considered. These problems are discussed and plausibility arguments are given to show that all clocks run in the same direction (almost always), that the most probable development of the Universe during the early stages of the expansion would result in the introduction of some internal organization, and that the expansion of the Universe and the increase in entropy define time directions that have the same sense. (...) The question of what properties of the laws governing the Universe lead to these results is studied. (shrink)

To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, but we show that (...) if the universe in not in thermodynamic equilibrium then it can he treated in terms of weakly interacting large scale constituents that are very nearly independent of each other. In this way we obtain the same results as those of the usual approach within the framework of the ontological interpretation. (shrink)

We present an analysis of Szilard's one-molecule Maxwell's demon, including a detailed entropy accounting, that suggests a general theory of the entropy cost of information. It is shown that the entropy of the demon increases during the expansion step, due to the decoupling of the molecule from the measurement information. It is also shown that there is an entropy symmetry between the measurement and erasure steps, whereby the two steps additivelv share a constant entropy change, but the proportion that occurs (...) during each of the two steps is arbitrary. Therefore the measurement step may be accompanied by an entropy increase, a decrease, or no change at all, and likewise for the erasure step. Generalizing beyond the demon, decorrelation between a physical system and information about that system always causes an entropy increase in the joint system comprised of both the original system and the information. Decorrelation causes a net entropy increase in the universe unless, as in the Szilard demon, the information is used to decrease entropy elsewhere before the correlation is lost. Thus, information is thermodynamically costly precisely to the extent that it is not used to obtain work from the measured system. (shrink)

A connection between two fundamental concepts of information and symmetry breaking (SB) is established. A concept called transform information (TI) is introduced. The known information measures (Hartley, von Neumann-Shannon-Wiener, Fisher informations, Renyi entropies) can be derived as (or mathematically expressed by) the particular forms of TI for certain transforms of a physical systems (when they are described by the probability measures). As TI is zero when the system is invariant under respective transform, it can be considered, when nonzero, as a (...) quantitative SB measure in the system under study. The classical information measures that are derived from TI also can be perceived as SB measures. This fact is a base for assigning a sense to information. The concept of TI is extended to the cases when systems are described without the use of probability concept. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

The thermodynamics of computation assumes that computational processes at the molecular level can be brought arbitrarily close to thermodynamic reversibility and that thermodynamic entropy creation is unavoidable only in data erasure or the merging of computational paths, in accord with Landauer’s principle. The no-go result shows that fluctuations preclude completion of thermodynamically reversible processes. Completion can be achieved only by irreversible processes that create thermodynamic entropy in excess of the Landauer limit.

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.

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 (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

Or better: time asymmetry in thermodynamics. Better still: time asymmetry in thermodynamic phenomena. “Time in thermodynamics” misleadingly suggests that thermodynamics will tell us about the fundamental nature of time. But we don’t think that thermodynamics is a fundamental theory. It is a theory of macroscopic behavior, often called a “phenomenological science.” And to the extent that physics can tell us about the fundamental features of the world, including such things as the nature of time, we generally think that only fundamental (...) physics can. On its own, a science like thermodynamics won’t be able to tell us about time per se. But the theory will have much to say about everyday processes that occur in time; and in particular, the apparent asymmetry of those processes. The pressing question of time in the context of thermodynamics is about the asymmetry of things in time, not the asymmetry of time, to paraphrase Price ( , ). I use the title anyway, to underscore what is, to my mind, the centrality of thermodynamics to any discussion of the nature of time and our experience in it. The two issues—the temporal features of processes in time, and the intrinsic structure of time itself—are related. Indeed, it is in part this relation that makes the question of time asymmetry in thermodynamics so interesting. This, plus the fact that thermodynamics describes a surprisingly wide range of our ordinary experience. We’ll return to this. First, we need to get the question of time asymmetry in thermodynamics out on the table. (shrink)

A critical discussion is provided of three central assumptions underlying Nunez's approach to modeling cortical activity. A plea is made for neurophysiologically realistic models involving nonlinearities, multiple time scales, and stochasticity.

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

This thesis analyses the ontological nature of quantum particles. In it I argue that quantum particles, despite their indistinguishability, are objects in much the same way as classical particles. This similarity provides an important point of continuity between classical and quantum physics. I consider two notions of indistinguishability, that of indiscernibility and permutation symmetry. I argue that neither sort of indistinguishability undermines the identity of quantum particles. I further argue that, when we understand in distinguishability in terms of permutation symmetry, (...) classical particles are just as indistinguishable as quantum particles; for classical physics also possesses permutation symmetry. (shrink)

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between (...) thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed. (shrink)

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

The process of recognition or isolation of one or several entities from among many possible entities is termed intellego perception. It is shown that not only are many of our everyday percepts of this type, but perception of microscopic events using the methods of quantum mechanics are also intellego in nature. Information theory seems to be a natural language in which to express perceptual activity of this type. It is argued that the biological organism quantifies its sensations using an information (...) theoretical measure. This, in turn, sets the stage for a mathematical theory of sensory perception. (shrink)

I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...) proposing a third modification of Lewis's theory, one which explains many of the common features shared by the chance theories of physics. (shrink)

Some of the most imaginative analyses in contemporary science have been fostered by the paradox of irreversibility. Rendered as a question the paradox reads: How can the anisotropic macrophysical behavior of a system of molecules be reconciled with the underlying reversible molecular model? Attempts to resolve and dissolve the paradox have appealed to large numbers of particles, jammed correlations, unseen perturbations, hidden variables or constraints, uncertainty principles, averaging procedures (e.g., coarse graining and time smoothing), stochastic flaws, cosmological origins, etc. While (...) acknowledging these efforts as important articulations of basic ideas of statistical mechanics, we question their relevance to irreversibility as it occurs in nature. It seems to us that once the emergence of the phenomenon of equilibrium is understood in terms of molecular dynamics, the macroscopic appearance of irreversibility can also be understood in terms of the frequency of forced withdrawals from young equilibria. We believe that the paradox of irreversibility can be resolved in a simple, logically clear, and aesthetically pleasing manner. (shrink)

I discuss a broad critique of the classical approach to the foundations of statistical mechanics (SM) offered by N. S. Krylov. He claims that the classical approach is in principle incapable of providing the foundations for interpreting the "laws" of statistical physics. Most intriguing are his arguments against adopting a de facto attitude towards the problem of irreversibility. I argue that the best way to understand his critique is as setting the stage for a positive theory which treats SM as (...) a theory in its own right, involving a completely different conception of a system's state. As the orthodox approach treats SM as an extension of the classical or quantum theories (one which deals with large systems), Krylov is advocating a major break with the traditional view of statistical physics. (shrink)

Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality (...) must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantum mechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantum mechanical wave function, and its environment by an appropriate potential profile, Schrödinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition. With these established, a number of the generic features of quantum mechanics, such as the wave/particle duality, and the uncertainty, indistinguishability, and exclusion principles, display metaphoric relevance to familiar individual and collective experiences. Similarly, such traditional quantum theoretic exercises as the central force field and atomic structure, covalent molecular bonds, barrier penetration, and quantum statistical collective behavior become useful analogies for representation of a variety of consciousness experiences, both normal and anomalous, and for the design of experiments to study these systematically. (shrink)

According to the principle of indifference, when a set of possibilities is evidentially symmetric for you – when your evidence no more supports any one of the possibilities over any other – you're required to distribute your credences uniformly among them. Despite its intuitive appeal, the principle of indifference is often thought to be unsustainable due to the problem of multiple partitions: Depending on how a set of possibilities is divided, it seems that sometimes, applying indifference reasoning can require you (...) to assign incompatible credences to equivalent possibilities. This paper defends the principle of indifference from the problem of multiple partitions by offering two guides for how to respond. The first is for permissivists about rationality, and is modeled on permissivists' arguments for the claim that a body of evidence sometimes does not uniquely determine a fully rational credence function. The second is for impermissivists about rationality, and is modeled on impermissivists' arguments for the claim that a body of evidence does always uniquely determine a fully rational credence function. What appears to be a decisive objection against the principle of indifference is in fact an instance of a general challenge taking different forms familiar to both permissivists and impermissivists. (shrink)

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 (...) effective theory, and we describe circumstances under which Gibbsian calculations coincide with the Boltzmannian results. We then point out that regarding GSM as an effective theory has important repercussions for a number of projects, in particular attempts to turn GSM into a nonequilibrium theory. (shrink)

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.

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 (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)

This paper addresses the question of how we should regard the probability distributions introduced into statistical mechanics. It will be argued that it is problematic to take them either as purely subjective credences, or as objective chances. I will propose a third alternative: they are "almost objective" probabilities, or "epistemic chances". The definition of such probabilities involves an interweaving of epistemic and physical considerations, and so cannot be classified as either purely subjective or purely objective. This conception, it will be (...) argued, resolves some of the puzzles associated with statistical mechanical probabilities; it explains how probabilistic posits introduced on the basis of incomplete knowledge can yield testable predictions, and it also bypasses the problem of disastrous retrodictions, that is, the fact the standard equilibrium measures yield high probability of the system being in equilibrium in the recent past, even when we know otherwise. As the problem does not arise on the conception of probabilities considered here, there is no need to invoke a Past Hypothesis as a special posit to avoid it. (shrink)

Based on Newton’s laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed universe oscillating in phase-space. We find that the behavior of this universe as a whole can be represented by a free entropic oscillator whose lifespan is nonhomogeneous, thus implying that time is shorter or longer according to the state of this universe given through its entropy. We conclude that time reduces to the entropy production of (...) this universe and that a nonzero entropy production means that local fluctuations could exist giving rise to the appearance of masses and to the curvature of the space. (shrink)

The nature of physical measurements performed on microscopic systems is discussed, and it is suggested that the procedures which are conventionally referred to as “measurements” fall into at least three different categories. The connection between observation processes and irreversible processes is stressed. The customary quantum mechanical treatment of irreversible processes is discussed, and its deficiencies from the philosophical point of view are criticized. The standpoint that quantum mechanics should not be considered as a basic philosophical system but rather as an (...) immensely useful “tool” is defended. Some attempts at developing a more “basic” theory are discussed, and a hypothesis is put forward concerning the role of entropy within some possible future nonlocal hidden-variable theory. (shrink)

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2012.

We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of macrostates forms the unique maximal partition of phase space which 1) is consistent with our observations (a subjective fact about our ability to observe the system) and 2) obeys a Markov process (an objective fact about the system's dynamics). We review the ideas of computational mechanics, (...) an information-theoretic method for finding optimal causal models of stochastic processes, and argue that macrostates coincide with the ``causal states'' of computational mechanics. Defining a set of macrostates thus consists of an inductive process where we start with a given set of observables, and then refine our partition of phase space until we reach a set of states which predict their own future, i.e. which are Markovian. Macrostates arrived at in this way are provably optimal statistical predictors of the future values of our observables. (shrink)