Statisticalmechanics 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 statisticalmechanics, the role of cosmology, the reduction of thermodynamics to statisticalmechanics, 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)
Statisticalmechanics attempts to explain the behaviour of macroscopic physical systems in terms of the mechanical properties of their constituents. Although it is one of the fundamental theories of physics, it has received little attention from philosophers of science. Nevertheless, it raises philosophical questions of fundamental importance on the nature of time, chance and reduction. Most philosophical issues in this domain relate to the question of the reduction of thermodynamics to statisticalmechanics. This book addresses issues (...) inherent in this reduction: the time-asymmetry of thermodynamics and its absence in statisticalmechanics; the role and essential nature of chance and probability in this reduction when thermodynamics is non-probabilistic; and how, if at all, the reduction is possible. Compiling contributions on current research by experts in the field, this is an invaluable survey of the philosophy of statisticalmechanics for academic researchers and graduate students interested in the foundations of physics. (shrink)
An investigation is made into how the foundations of statisticalmechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These (...) imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time. (shrink)
This paper is a discussion of David Albert's approach to the foundations of classical statistical menchanics. I point out a respect in which his account makes a stronger claim about the statistical mechanical probabilities than is usually made, and I suggest what might be motivation for this. I outline a less radical approach, which I attribute to Boltzmann, and I give some reasons for thinking that this approach is all we need, and also the most we are likely (...) to get. The issue between the two accounts turns out to be one about the explanatory role probabilities play in statisticalmechanics. (shrink)
Is thermodynamics true of self-gravitating systems? Or better put, does equilibrium statisticalmechanics, the theory describing the microscopic basis of thermal phenomena, apply when the dominant coupling in a system is via (classical) gravitation? This question is the subject of increasing interest in astrophysics, but it is rarely pursued from a foundational perspective.[1] From this standpoint, the issue is not only fascinating in its own right, but it is an important prism through which to view other foundational projects (...) in statisticalmechanics. By considering it, we increase our understanding of the conditions under which a thermodynamic description of the world can emerge. (shrink)
Discussions of the foundations of Classical Equilibrium StatisticalMechanics (SM) typically focus on the problem of justifying the use of a certain probability measure (the microcanonical measure) to compute average values of certain functions. One would like to be able to explain why the equilibrium behavior of a wide variety of distinct systems (different sorts of molecules interacting with different potentials) can be described by the same averaging procedure. A standard approach is to appeal to ergodic theory to (...) justify this choice of measure. A different approach, eschewing ergodicity, was initiated by A. I. Khinchin. Both explanatory programs have been subjected to severe criticisms. This paper argues that the Khinchin type program deserves further attention in light of relatively recent results in understanding the physics of universal behavior. (shrink)
During a long and distinguished career, Belgian physical chemist Ilya Prigogine (1917–2003) pursued a coherent research program in thermodynamics, statisticalmechanics, and related scientific areas. The main goal of this effort was establishing the origin of thermodynamic irreversibility (the ‘‘arrow of time’’) as local (residing in the details of the interaction of interest), rather than as global (being solely a consequence of properties of the initial singularity – the ‘‘Big Bang’’). In many publications for general audiences, he stated (...) the opinion that this scientific research had great philosophical importance. Prigogine and his colleagues considered that the most recent stages of this research program have been successful, so that the local origins of the arrow of time are now established. There is no scientific consensus as to whether or not this claim is valid. Similarly, there is no consensus on whether the competing global (initial singularity) explanation has been proven. (shrink)
We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statisticalmechanics. Our claim is based on the observations that dynamical systems for which statisticalmechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the (...) behaviour must ensure that the approach to equilibrium for these observables is on the appropriate time-scale. (shrink)
In this paper we address two problems in Boltzmann's approach to statisticalmechanics. The first is the justification of the probabilistic predictions of the theory. And the second is the inadequacy of the theory's retrodictions.
In two recent papers Barry Loewer ( 2001 , 2004 ) has suggested to interpret probabilities in statisticalmechanics as chances in David Lewis’s ( 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. †To contact the author, please write to: Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics, (...) Houghton Street, London WC2A 2AE, England; e‐mail: r.p.frigg@lse.ac.uk. (shrink)
The fundamental problem on which Ilya Prigogine and the Brussels- Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of (...) time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statisticalmechanics remains the same, their more recent approach addresses the physical features of large Poincar´. (shrink)
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution on its phase space, (...) of its thermodynamic entropy with the Gibbs entropy of , and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statisticalmechanics – are thoroughly misguided. (shrink)
The traditional use of ergodic theory in the foundations of equilibrium statisticalmechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination (...) of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well-known that this account is problematic.
This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented. (shrink)
Huw Price (1996, 2002, 2003) argues that causal-dynamical theories that aim to explain thermodynamic asymmetry in time are misguided. He points out that in seeking a dynamical factor responsible for the general tendency of entropy to increase, these approaches fail to appreciate the true nature of the problem in the foundations of statisticalmechanics (SM). I argue that it is Price who is guilty of misapprehension of the issue at stake. When properly understood, causal-dynamical approaches in the foundations (...) of SM offer a solution for a different problem; a problem that unfortunately receives no attention in Price’s celebrated work. (shrink)
StatisticalMechanics (SM) involves probabilities. At the same time, most approaches to the foundations of SM—programs whose goal is to understand the macroscopic laws of thermal physics from the point of view of microphysics—are classical; they begin with the assumption that the underlying dynamical laws that govern the microscopic furniture of the world are (or can without loss of generality be treated as) deterministic. This raises some potential puzzles about the proper interpretation of these probabilities. It also raises, (...) more generally, the question of what kinds, if any, of objective probabilities can exist in a deterministic world. (shrink)
This paper explores some connections between competing conceptions of scientific laws on the one hand, and a problem in the foundations of statisticalmechanics on the other. I examine two proposals for understanding the time asymmetry of thermodynamic phenomenal: David Albert's recent proposal and a proposal that I outline based on Hans Reichenbach's “branch systems”. I sketch an argument against the former, and mount a defense of the latter by showing how to accommodate statisticalmechanics to (...) recent developments in the philosophy of scientific laws. (shrink)
In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statisticalmechanics 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.
I discuss a broad critique of the classical approach to the foundations of statisticalmechanics (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)
A serious flaw in Hartry Field’s instrumental account of applied mathematics, namely that Field must overestimate the extent to which many of the structures of our mathematical theories are reflected in the physical world, underlies much of the criticism of this account. After reviewing some of this criticism, I illustrate through an examination of the prospects for extending Field’s account to classical equilibrium statisticalmechanics how this flaw will prevent any significant extension of this account beyond field theories. (...) I note in the conclusion that this diagnosis of Field’s program also points the way to modifications that may work. (shrink)
This article distinguishes two different senses of information-theoretic approaches to statisticalmechanics that are often conflated in the literature: those relating to the thermodynamic cost of computational processes and those that offer an interpretation of statisticalmechanics where the probabilities are treated as epistemic. This distinction is then investigated through Earman and Norton’s ([1999]) ‘sound’ and ‘profound’ dilemma for information-theoretic exorcisms of Maxwell’s demon. It is argued that Earman and Norton fail to countenance a ‘sound’ information-theoretic (...) interpretation and this paper describes how the latter inferential interpretations can escape the criticisms of Earman and Norton ([1999]) and Norton ([2005]) by adopting this ‘sound’ horn. This article considers a standard model of Maxwell’s demon to illustrate how one might adopt an information-theoretic approach to statisticalmechanics without a reliance on Landauer’s principle, where the incompressibility of the probability distribution due to Liouville’s theorem is taken as the central feature of such an interpretation. (shrink)
In this paper I first argue that the objection which is most commonly levelled against the coarse-graining approach-viz. that it introduces an element of subjectivity into what ought to be a purely objective formalism-is ultimately unfounded. I then proceed to argue that two different objections to the coarse-graining approach indicate that it is an inadequate approach to statisticalmechanics. The first objection is based on the fact that the appeal to appearances by the coarse-graining approach fails to justify (...) the coarse-graining strategy of ignoring the physical differences between so-called quasi-equilibrium distributions and equilibrium distributions. The second objection is centred on the notion of a coarse-grained entropy. I will argue that the required increase in the coarse-grained entropy is obtained by disregarding the dynamical constraints on the system. This undermines the very task statisticalmechanics has set out to accomplish, viz. to provide a microdynamical underpinning of thermodynamics. (shrink)
Why does classical equilibrium statisticalmechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcanonical exist. In response I define the generalized properties of epsilon-ergodicity and epsilon-continuity, I review computational evidence indicating that systems of interest are epsilon-ergodic, I adapt Malament (...) and Zabell’s defense of absolute continuity to support epsilon-continuity, and I prove that, for epsilon-ergodic systems, every epsilon-continuous invariant probability measure is very close to the microcanonical. (shrink)
An important contemporary version of Boltzmannian statisticalmechanics 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. I give a precise formulation of the proposal and present an argument in support of its central contention. †To contact the author, please write to: Department of Philosophy, Logic, and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, England; e‐mail: r.p.frigg@lse.ac.uk. (shrink)
Interventionism is an approach to the foundations of statisticalmechanics which says that to explain and predict some of the thermodynamic phenomena we need to take into account the inescapable effect of environmental perturbations on the system of interest, in addition to the system's internal dynamics. The literature on interventionism suffers from a curious dual attitude: the approach is often mentioned as a possible framework for understanding statisticalmechanics, only to be quickly and decidedly dismissed. The (...) present paper is an attempt to understand this attraction-repulsion story. It offers a version of interventionism that appears to be defensible, and shows that this version can meet the main objections raised against it. It then investigates some of the philosophical ideas underlying interventionism, and proposes that these may be the source of the resentment interventionism encounters. This paves the way to see some features and consequences of interventionism, often taken to be shortcomings, as philosophically advantageous. (shrink)
El propósito del presente artículo es evaluar en qué sentido y bajo qué condiciones la ergodicidad es relevante para explicar el éxito de la mecánica estadística. Se objeta la positión de quienes sostienen que la ergodicidad es irrelevante para tal explicatión, y se señala que las propiedades ergódicas desempeñan diferentes papeles en la mecánica estadística del equilibrio y en la descriptión de la evolución hacia el equilibrio: es posible prescindir de la ergodicidad en el primer caso pero no en el (...) segundo. Sobre esta base, se reformularán las definiciones de ergodicidad y mezcla, relativizándolas a la macrovariable particular cuya evolución irreversible se desea describir. Finalmente, se enfatiza la importancia de tomar en cuenta la elaboratión de modelos para evaluar la utilizatión de los métodos de Gibbs. /// The aim of this paper is to consider in what sense and under what conditions ergodicity is relevant for explaining the success of StatisticalMechanics. We argue against those who claim that ergodicity is irrelevant to this explanation, by noting that ergodic properties play different roles in equilibrium StatisticalMechanics and in the description of the approach to equilibrium: it is possible to do without it in the first case but not in the second one. On this basis, we reformulate the definitions of ergodicity and mixing, relativizing them to the particular macrovariable whose irreversible evolution is to be described. Finally, we stress the relevance of taking into account model-construction for evaluating the use of Gibbs' methods. (shrink)
In the usual procedure of deriving equilibrium thermodynamics from classical statisticalmechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to (...) account for the non-equilibrium part of the laws of thermodynamics. Rather, we have to weaken the requirement that equilibrium be identified with a stationary probability distribution. (shrink)
During the last decade, the interaction based models have received increased attention in economics, mainly with the recognition that modeling aggregate patterns of behavior requires viewing individuals in their social environments continuously in interaction with each other. The existing literature suggests that statisticalmechanics tools can be useful to model interactions among economic agents. In addition to statisticalmechanics, the network approach has also gained popularity, as is evident in the rising attention attributed to small world (...) models and scale free network topologies. These developments point to the fact that interdisciplinary research in economics, mainly using the tools of physics has accelerated to a great extent. In this paper, we review the analogies made between molecules and economic agents in statisticalmechanics models, as they are utilized in economics literature. We perform a simulation study by using the small world model and statisticalmechanics, to demonstrate the influence of network structure in the spreading of organizational forms, in particular the research collaboration decisions of firms. (shrink)
This second part of a two-part essay discusses recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their similarity transformation approach (see Part I), but the contemporary approach utilizes rigged Hilbert space (whereas the older approach used Hilbert space). While the emphasis on nonequilibrium statisticalmechanics remains the same, the use of similarity transformations shifts to the background. In its place arose an interest in the physical features of large (...) Poincaré systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)
It is argued that the so-called minimal statistical interpretation of quantum mechanics does not completely resolve the measurement problem in that this view is unable to show that quantjum mechanics can dispense with classical physics when it comes to a treatment of the measuring interaction. It is suggested that the view that quantum mechanics applies to individual systems should not be too hastily abandoned, in that this view gives perhaps the best hope of leading to a (...) version of quantum mechanics which does provide a complete solution to the measurement problem. (shrink)
I argue against the claim, advanced by David Albert and Barry Loewer, that all non-fundamental laws can be derived from those required to underwrite the second law of thermodynamics.
The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized (...) by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium. (shrink)
Consider a …nite collection of marbles. The statement "half the marbles are white" is about counting, and not about the probability of drawing a white marble from the collection. The question is whether nonprobabilistic counting notions such as half, or vast majority can make sense, and preserve their meaning when extended to the realm of the continuum. In this paper we argue that the Lebesgue measure provides the proper non-probabilistic extension, which is as natural, and in a sense uniquely forced, (...) as the extension of the concept of cardinal number to in…nite sets by Cantor. To accomplish this a di¤erent way of constructing the Lebesgue measure is applied. One important example of a non-probabilistic counting concept is typicality, introduced to statistical physics to explain the approach to equilibrium. A typical property is shared by a vast majority of cases. Typicality is not probabilistic, at least in the sense that it is robust and not dependent on any precise assumptions about the probability distribution. A few dynamical assumptions together with the extended counting concepts do explain the approach to equilibrium. The explanation though is a weak one, and in itself allows for no speci…c predictions about the behavior of a system within a reasonably bounded time interval. It is also argued that typicality is too weak a concept and one should stick with the fully ‡edged Lebesgue measure. We show that typicality is not a logically closed concept. For example, knowing that two ideally in…nite data sequences are typical does not guarantee that they make a typical pair of sequences, whose correlation is well de…ned. Thus, to explain basic statistical regularities we need an independent concept of typical pair, which cannot be de…ned without going back to a construction of the Lebesgue measure on the set of pairs. To prevent this and other problems we can hold on to the Lebesgue measure itself as the basic construction. (shrink)
The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized (...) by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium. (shrink)
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: one that teaches us something about the connection between the asymmetry of (...) overdetermination and the asymmetry of entropy. (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.
We present a brief history of decoherence, from its roots in the foundations of classical statisticalmechanics, to the current spin bath models in condensed matter physics. We analyze the philosophical import of the subject matter in three different foundational problems, and find that, contrary to the received view, decoherence is less instrumental to their solutions than it is commonly believed. What makes decoherence more philosophically interesting, we argue, are the methodological issues it draws attention to, and the (...) question of the universality of quantum mechanics. (shrink)
In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it is then made (...) in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. The intended result is to induce a deeper appreciation of the complexity and fruitfulness of idealization in the praxis of model-building, not to give an abstract theory of it. (shrink)
In this paper, possible objections to the propensity microrealistic version of quantum mechanics proposed in Part I are answered. This version of quantum mechanics is compared with the statistical, particle microrealistic viewpoint, and a crucial experiment is proposed designed to distinguish between these to microrealistic versions of quantum mechanics.
A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann's H-theorem, and its simplified variant in the Ehrenfests' 1912 wind-tree model. The little-cited 1896 (pre-recurrence) objection of Zermelo (similar to an 1889 argument due to Poincare) is also analysed. Significant differences between the objections are highlighted, and several old and modern misconceptions concerning both them and the H-theorem are clarified. We give (...) particular emphasis to the radical nature of Poincare's and Zermelo's attack, and the importance of the shift in Boltzmann's thinking in response to the objections as a whole. (shrink)
According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low entropy macrostates are less probable than high entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law of thermodynamics is fundamentally flawed, and will show that some puzzles sometimes associated with the second (...) law are merely artifacts of this incorrect justification. (shrink)
According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the (...) second law are merely artifacts of this questionable justification. *Received October 2006; revised October 2007. †To contact the author, please write to: Department of Philosophy, University of Chicago, 1115 E. 58th St., Chicago, IL 60637; e-mail: kjdavey@uchicago.edu. (shrink)
In their book The Road to Maxwell's Demon Hemmo & Shenker re-describe the foundations of statisticalmechanics from a purely empiricist perspective. The result is refreshing, as well as intriguing, and it goes against much of the literature on the demon. Their conclusion, however, that Maxwell's demon is consistent with statisticalmechanics, still leaves open the question of why such a demon hasn't yet been observed on a macroscopic scale. This essay offers a sketch of what (...) a possible answer could look like. (shrink)
The distribution function associated with a classical gas at equilibrium is considered. We prove that apart from a factorisable multiplier, the distribution function is fully determined by the correlations among local momenta fluctuations. Using this result we discuss the conditions which enable idealised local observers, who are immersed in the gas and form a part of it, to determine the distribution 'from within'. This analysis sheds light on two views on thermodynamic equilibrium, the 'ergodic' and the 'thermodynamic limit' schools, and (...) the relations between them. It also provides an outline for a new definition of equilibrium that is weaker than full ergodicity. Finally, we briefly discuss the possibility that the distribution can be determined by external observers. (shrink)
The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon and to develop a mathematical formalism that can describe this direction as being due to the dynamics of physical systems. In part I of this essay, I review and assess an attempt to carry out an approach that received much of their attention from the early 1970s to the mid 1980s. In part II, I will discuss their more recent approach using rigged Hilbert spaces. (shrink)
This commentary focuses on how bottom-up neocortical models can be developed into eigenfunction expansions of probability distributions appropriate to describe short-term memory in the context of scalp EEG. The mathematics of eigenfunctions are similar to the top-down eigenfunctions developed by Nunez, despite different physical manifestations. The bottom-up eigenfunctions are at the local mesocolumnar scale, whereas the top-down eigenfunctions are at the global regional scale. Our respective approaches have regions of substantial overlap, and future studies may expand top-down eigenfunctions into the (...) bottom-up eigenfunctions, yielding a model of scalp EEG expressed in terms of columnar states of neocortical processing of attention and short-term memory. Footnotes1 The author is also affiliated with DRW Investments LLC, 311 S. Wacker Drive, Chicago, IL 60606. (shrink)
An intricate, long, and occasionally heated debate surrounds Boltzmann’s H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt’s 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the (...) first part, I discuss the development of Boltzmann’s research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt’s challenge and Boltzmann’s response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject. (shrink)
I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it is (...) not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. (shrink)
Several proponents of the interventionist theory of causation have recently argued for a neo-Russellian account of causation. The paper discusses two strategies for interventionists to be neo-Russellians. Firstly, I argue that the open systems argument – the main argument for a neo-Russellian account advocated by interventionists – fails. Secondly, I explore and discuss an alternative for interventionists who wish to be neo-Russellians: the statistical mechanical account. Although the latter account is an attractive alternative, it is argued that interventionists are (...) not able to adopt it straightforwardly. Hence, to be neo-Russellians remains a challenge to interventionists. (shrink)
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 statisticalmechanics, and discusses (...) the indifference approach to statistical mechanical probabilities. (shrink)
Contents: 1. The concept of chance; 2. The classical picture; 3. Ways the world might be; 4. Possibilities of thought; 5. Chance in phase space; 6. Possibilist theories of chance; 7. Actualist theories of chance; 8. Anti-realist theories of chance; 9. Chance in quantum physics; 10. Chance in branching worlds; 11. Time and evidence; 12. Debunking chance.
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 second of these articles discusses the regularity approach to statistical mechanical probabilities, and describes (...) some areas where further research is needed. (shrink)
I examine different arguments that could be used to establish indeterminism of neurological processes. Even though scenarios where single events at the molecular level make the difference in the outcome of such processes are realistic, this falls short of establishing indeterminism, because it is not clear that these molecular events are subject to quantum mechanical uncertainty. Furthermore, attempts to argue for indeterminism autonomously (i.e., independently of quantum mechanics) fail, because both deterministic and indeterministic models can account for the empirically (...) observed behavior of ion channels. (shrink)
It is argued that certain recent advances in the construction of a theory of the collapses of Quantum Mechanical wave functions suggest the possibility of new and improved foundations for statisticalmechanics, foundations in which epistemic considerations play no role.
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 statisticalmechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statisticalmechanics 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)
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 statisticalmechanics, 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)
Some philosphers of science of an empiricist and pragmatist bent have proposed models of statistical explanation, but have then become sceptical of the adequacy of these models. It is argued that general considerations concerning the purpose of function of explanation in science which are usually appealed to by such philosophers show that their scepticism is not well taken; for such considerations provide much the same rationale for the search for statistical explanations, as these philosophers have characterized them, as (...) they do for lawlike explanations. But, it is further argued, a significant piece of what is frequently offered as an explanation of well known phenomena in statisticalmechanics, fails to meet this general "pragmatic rationale" for statistical, or indeed any kind of, explanation. The question then arises whether the physicists have misconstrued the value of this piece of physical theorizing, ergodic theory, taking it to be explanatory when it is actually not; or whether, instead, the philosopher's account of just what is genuinely explanatory is too narrow. (shrink)
The problem of relation between statisticalmechanics (SM) and classical mechanics (CM), especially the question whether SM can be founded on CM, has been a subject of controversies since the rise of classical statisticalmechanics (CSM) at the end of 19th century. The first views rejecting explicitly the possibility of laying the foundations of CSM in CM were triggered by the "Wiederkehr-" and "Umkehreinwand" arguments. These arguments played an important role in the debate about Boltzmann's (...) original H-theorem and led to the so called statistical H-theorem proposed by Boltzmann himself. (For the history of these early debates we refer to Brush's monograph (Brush 1976).) After CSM had been brought to "canonical form" by the Ehrenfests, (Ehrenfest and Ehrenfest 1959) the physicists turned away from the foundational problem leaving it to mathematicians to worry about in the form of what has become called the ergodic theory. In retrospect, the physicists' general mood seems to have been the hope that ergodic theory establishes rigorously what is needed to found CSM on CM and which had been expressed essentially by Boltzmann already (Wightman 1985). However, very few physicists followed closely the developments in the mathematical theory of dynamic systems. One of those who did was the Russian physicist N.S. Krylov. (For a brief description of Krylov's personal life we refer to the papers in (Krylov 1979).). (shrink)
In quantum mechanics, the expression for entropy is usually taken to be -kTr(ln), where is the density matrix. The convention first appears in Von Neumann's Mathematical Foundations of Quantum Mechanics. The argument given there to justify this convention is the only one hitherto offered. All the arguments in the field refer to it at one point or another. Here this argument is shown to be invalid. Moreover, it is shown that, if entropy is -kTr(ln), then perpetual motion machines (...) are possible. This and other considerations support the conclusion that this expression is not the quantum-mechanical correlate of thermodynamic entropy. Its usefulness in quantum-statisticalmechanics can be explained by its being a convenient quantification of information, but information and entropy are not synonymous. As the present paper shows, one can change while the other is conserved. (shrink)
In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we have addressed the mechanical foundations of equilibrium thermodynamics on the basis of the Generalized Helmholtz Theorem. It was found that the volume entropy provides a good mechanical analogue of thermodynamic entropy because it satisfies the heat theorem and it is an adiabatic invariant. This property explains the ``equal'' sign in Clausius principle ($S_f \geq S_i$) in a purely mechanical way and suggests that the volume entropy (...) might explain the ``larger than'' sign (i.e. the Law of Entropy Increase) if non adiabatic transformations were considered. Based on the principles of microscopic (quantum or classical) mechanics here we prove that, provided the initial equilibrium satisfy the natural condition of decreasing ordering of probabilities, the expectation value of the volume entropy cannot decrease for arbitrary transformations performed by some external sources of work on a insulated system. This can be regarded as a rigorous quantum mechanical proof of the Second Law. We discuss how this result relates to the Minimal Work Principle and improves over previous attempts. The natural evolution of entropy is towards larger values because the natural state of matter is at positive temperature. Actually the Law of Entropy Decrease holds in artificially prepared negative temperature systems. (shrink)
PHILOSOPHY OF SCIENCE, vol. 52, number 1, pp.44-63. R.M. Nugayev, Kazan State |University, USSR. -/- THE HISTORY OF QUANTUM THEORY AS A DECISIVE ARGUMENT FAVORING EINSTEIN OVER LJRENTZ. -/- Abstract. Einstein’s papers on relativity, quantum theory and statisticalmechanics were all part of a single research programme ; the aim was to unify mechanics and electrodynamics. It was this broader program – which eventually split into relativistic physics and quantummmechanics – that superseded Lorentz’s theory. The argument of (...) this paper is partly historical and partly methodological. A notion of “crossbred objects” – theoretical objects with contradictory properties which are part of the domain of application of two different research programs – is developed that explains the dynamics of revolutionary theory change. (shrink)
This paper presents a general formal semantic scheme for the interpretation of quantum mechanics, in terms of which van Fraassen's Copenhagen and anti-Copenhagen variants of the modal interpretation are examined. The general character of the modal interpretation is motivated in a discussion of classical statisticalmechanics, the distinction being made between statistical states and micro-states. The notion of a quasi-classical (micro) state is introduced in a discussion of the theorem of Gleason and Kochen and Specker. It (...) is shown that, according to the anti-Copenhagen variant, the class of micro-states coincides with a special class of quasi-classical states. The paper concludes with two general criticisms of the anti-Copenhagen variant. (shrink)
