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

In a world awash in statistical patterns, should we conclude that the universe’s evolution or genesis is somehow subject to chance? I draw attention to alternatives that must be acknowledged if we are to have an adequate assessment of what chance the universe might have had.

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests (...) interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics. (shrink)

Exposed in 1948, within his masterpiece on the scope and limits of human knowledge, the epistemological tenets that Bertrand Russell regarded as fundamental elements in the construction of scientific knowledge, are still worthy of a detailed discussion today. Given the excellence of the author, it will not be surprising to see that Russell's gnoseologic postulates, even for the present scientific view, address some of the most controversial questions still to be solved in the theory of knowledge.

The paper discusses the recent literature on abstraction/idealization in connection with the “paradox of infinite idealization.” We use the case of taking thermodynamics limit in dealing with the phenomena of phase transition and critical phenomena to broach the subject. We then argue that the method of infinite idealization is widely used in the practice of science, and not all uses of the method are the same. We then confront the compatibility problem of infinite idealization with scientific realism. We propose and (...) defend a contextualist position for realism and argue that the cases for infinite idealization appear to be fully compatible with contextual realism. (shrink)

Ludwig Boltzmann is one of the foremost responsible for the development of modern atomism in thermodynamics. His proposition was revolutionary not only because it brought a new vision for Thermodynamics, merging a statistical approach with Newtonian physics, but also because he produced an entirely new perspective on the way of thinking about and describing physical phenomena. Boltzmann dared to flirt with constructivism and realism simultaneously, by hypothesizing the reality of atoms and claiming an inherent probabilistic nature related to many particles (...) systems. Boltzmann faced criticism from the positivists, who rejected the hypothesis of the atom as a matter of principle, and also from physicists, who rejected the idea of a classical bounded system that does not follow deterministic mechanical laws. We consider that Boltzmann thermodynamics has emerged as a systemic theory that deals with macroscopic bodies using collective variables; it was reformulated to a kinetic theory of gases, and subsequently to statistical mechanics. From the theoretical physical point of view, Boltzmann advocates an approach to thermodynamics based on mechanics and was one of the founders of statistical mechanics, together with ideas by Maxwell, Clausius and Gibbs. Subsequently, statistical mechanics has also influenced the development of quantum mechanics and information theory. Using an evolutionary epistemological perspective as a metaphor to describe the physical entities claimed in Boltzmann propositions, we interpret his work as a selected theory that gained attributes of reality and “survived” during a scientific-contextual competition to be more adapted, in the sense that it was able to better explain physical phenomena, and also generated “descendants”. (shrink)

The foundation of statistical mechanics and the explanation of the success of its methods rest on the fact that the theoretical values of physical quantities (phase averages) may be compared with the results of experimental measurements (infinite time averages). In the 1930s, this problem, called the ergodic problem, was dealt with by ergodic theory that tried to resolve the problem by making reference above all to considerations of a dynamic nature. In the present paper, this solution will be analyzed first, (...) highlighting the fact that its very general nature does not duly consider the specificities of the systems of statistical mechanics. Second, Khinchin’s approach will be presented, that starting with more specific assumptions about the nature of systems, achieves an asymptotic version of the result obtained with ergodic theory. Third, the statistical meaning of Khinchin’s approach will be analyzed and a comparison between this and the point of view of ergodic theory is proposed. It will be demonstrated that the difference consists principally of two different perspectives on the ergodic problem: that of ergodic theory puts the state of equilibrium at the center, while Khinchin’s attempts to generalize the result to non-equilibrium states. (shrink)

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian (...) conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality. (shrink)

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)

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)