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)

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)

The term philosophy of chemistry is here construed broadly to include some publications from the history of chemistry and chemical education. Of course this initial selection of material has inevitably been biased by the interests of the author. This bibliography supersedes that of van Brakel and Vermeeren (1981), although no attempt has been made to include every single one of their entries, especially in languages other than English. Also, readers interested particularly in articles in German may wish to consult the (...) bibliography by Dittus and Mayer which also contains some material not included here (Dittus and Mayer, 1992). The aim is to maintain an up-to-date version of this bibliography and to publish a revised version in due course. Suggestions for further inclusions should be sent to the author. (shrink)

In this paper, I analyze the physical content of the main information concepts in the history of physics of the last seven decades. I argue that this physical character should be evaluated not by appealing to analytical-linguistic confusion (Timpson 2013) or to the usefulness of its applicability (Lombardi et al. 2016), but properly from its capacity to allow us to acquire significant knowledge about the physical world. After systematically employing this epistemic criterion of physical significance I will conclude by rejecting (...) the main strategies of ontological inflation and physical content of the main information concepts in the classical thermal physics literature. (shrink)

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)

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)

In this paper I will defend the incapacity of the informational frameworks in thermal physics, mainly those that historically and conceptually derive from the work of Brillouin (1962) and Jaynes (1957a), to robustly explain the approach of certain gaseous systems to their state of thermal equilibrium from the dynamics of their molecular components. I will further argue that, since their various interpretative, conceptual and technical-formal resources (e.g. epistemic interpretations of probabilities and entropy measures, identification of thermal entropy as Shannon information, (...) and so on) are shown to be somehow incoherent, inconsistent or inaccurate, these informational proposals need to 'epistemically parasitize' the manifold of theoretical resources of Boltzmann's and Gibbs' statistical mechanics, respectively, in order to properly account for the equilibration process of an ideal gas from its microscopic properties. Finally, our conclusion leads us to adopt a sort of constructive skepticism regarding the explanatory value of the main informationalist trends in statistical thermophysics. (shrink)

The search for the statistical mechanical underpinning of thermodynamic irreversibility has so far focussed on the spontaneous approach to equilibrium. But this is the search for the underpinning of what Brown and Uffink have dubbed the ‘minus first law’ of thermodynamics. In contrast, the second law tells us that certain interventions on equilibrium states render the initial state ‘irrecoverable’. In this article, I discuss the unusual nature of processes in thermodynamics, and the type of irreversibility that the second law embodies. (...) I then search for the microscopic underpinning or statistical mechanical ‘reductive basis’ of the second law of thermodynamics by taking a functionalist strategy. First, I outline the functional role of the thermodynamic entropy: for a thermally isolated system, the thermodynamic entropy is constant in quasi-static processes, but increasing in non-quasi-static processes. I then search for the statistical mechanical quantity that plays this role—rather than the role of the traditional ‘holy grail’ as described by Callender. I argue that in statistical mechanics, the Gibbs entropy plays this role. (shrink)

En este artículo pretendo evaluar las bases conceptuales y interpretativas de las ‘paradojas info-térmicas’ subyacentes a las aproximaciones informacionales a la física térmica, por las cuales nuestra información epistémica sobre un sistema molecular aumenta y disminuye simultáneamente cuando este se aproxima al equilibrio térmico. Defiendo que el contenido paradójico de nuestra tesis persiste incluso cuando se distinguen distintos tipos de información, debido a la conexión robusta entre la parte del incremento y la parte de la disminución informacional de la tesis. (...) Concluiré defendiendo que dicha paradoja muestra las inconsistencias conceptuales de las aproximaciones informacionales de la física térmica. (shrink)

Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences φ and θ, we consider the structures with domain {1,..., N} that satisfy θ, and compute the fraction of them in which φ is true. We then consider what happens to this fraction as N gets large. This extends the work on 0-1 laws that considers the limiting probability of first-order sentences, by considering asymptotic conditional (...) probabilities. As shown by Liogon'kii [24], if there is a non-unary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We extend this result to show that asymptotic conditional probabilities do not always exist for any reasonable notion of limit. Liogon'kii also showed that the problem of deciding whether the limit exists is undecidable. We analyze the complexity of three problems with respect to this limit: deciding whether it is well-defined, whether it exists, and whether it lies in some nontrivial interval. Matching upper and lower bounds are given for all three problems, showing them to be highly undecidable. (shrink)

In this survey, we discuss and analyze foundational issues of the problem of time and its asymmetry from a unified standpoint. Our aim is to discuss concisely the current theories and underlying notions, including interdisciplinary aspects, such as the role of time and temporality in quantum and statistical physics, biology, and cosmology. We compare some sophisticated ideas and approaches for the treatment of the problem of time and its asymmetry by thoroughly considering various aspects of the second law of thermodynamics, (...) nonequilibrium entropy, entropy production, and irreversibility. The concept of irreversibility is discussed carefully and reanalyzed in this connection to clarify the concept of entropy production, which is a marked characteristic of irreversibility. The role of boundary conditions in the distinction between past and future is discussed with attention in this context. The paper also includes a synthesis of past and present research and a survey of methodology. It also analyzes some open questions in the field from a critical perspective. (shrink)

In this essay I critically examine the role of entropy of mixing in articulating a macroscopic criterion for the sameness and difference of chemical substances. Consider three cases of mixing in which entropy change occurs: isotopic variants, spin isomers, and populations of atoms in different orthogonal quantum states. Using these cases I argue that entropy of mixing tracks differences between physical states, differences that may or may not correspond to a difference of substance. It does not provide a criterion for (...) the sameness and difference of substance that is appropriate to chemistry. (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)

A number of areas of biology raise questions about what is of value in the natural environment and how we ought to behave towards it: conservation biology, environmental science, and ecology, to name a few. Based on my experience teaching students from these and similar majors, I argue that the field of environmental ethics has much to teach these students. They come to me with pent-up questions and a feeling that more is needed to fully engage in their subjects, and (...) I believe some exposure to environmental ethics can help focus their interests and goals. I identify three primary areas in which environmental ethics can con- tribute to their education. The first is an examination of who (or what) should be considered to be part of our moral community (i.e., the community to whom we owe direct duties). Is it humans only? Or does it include all sentient life? Or all life? Or ecosystems considered holistically? Often, readings implicitly assume one or more of these answers; the goal is to make the student more sensitive to these implicit claims and to get them to think about the different reasons that support them. The second area, related to the first, is the application of the different answers concerning the extent of the ethical community to real environmental issues and problems. Students need to be aware of how the different answers concerning the moral community can imply conflicting answers for how we should act in certain cases and to think about ways to move toward conflict resolution. The third area in which environmental ethics can contribute is a more conceptual one, focusing on central concepts such as biodiversity, sustainability, species, and ecosystems. Exploring and evaluating various meanings of these terms will make students more reflective and thoughtful citizens and biologists, sensitive to the implications that different conceptual choices make. (shrink)

A statistical mechanical treatment is given of thermal contact between two systems. Reciprocal temperature emerges from this as the relative change in the number of microscopic states a macroscopic system at equilibrium ranges over, at constant volume and chemical composition, with change in internal energy. The significance of this is discussed in detail with reference to a monatomic gas and an Einstein solid.

We introduce a simple model for so-called spin-echo experiments. We show that the model is a mincing system. On the basis of this model we study fine-grained entropy and coarse-grained entropy descriptions of these experiments. The coarse-grained description is shown to be unable to provide an explanation of the echo signals, as a result of the way in which it ignores dynamically generated correlations. This conclusion is extended to the general debate on the foundations of statistical mechanics. We emphasize the (...) need for an appropriate mechanism to explain the gradual suppression over time of the correlations in a thermodynamic system. We argue that such a mechanism can only be provided by the interventionist approach, in which the interaction of the system with its environment is taken into account. Irreversible behavior is then seen to arise not as a result of limited measurement accuracy , but as a result of the fact that thermodynamic systems are limited systems which interact with their environment. A detailed discussion is given of recent objections to the interventionist approach in the literature. (shrink)

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

The rationality of scientific concept formation in theory transitions, challenged by the thesis of semantic incommensurability, can be restored by theChains of Meaning approach to concept formation. According to this approach, concepts of different, succeeding theories may be identified with respect to referential meaning, in spite of grave diversity of the mathematical structures characterizing them in their respective theories. The criterion of referential identity for concepts is that they meet a relation ofsemantic embedding, i.e. that the embedding concept can be (...) substituted by the embedded one in classical limit situations. Three case studies from contemporary physics theories will be used to show that the Chains of Meaning approach not only yields meaning comparisons for already established concepts (as for Newtonian and Schwarzschild mass) but is also well suited to characterize actual scientific strategies of concept formation in yet open cases such as black hole entropy or relativistic thermodynamics. (shrink)