Compendium of the foundations of classical statistical physics

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.
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Jill North (2010). An Empirical Approach to Symmetry and Probability. Studies in History and Philosophy of Science Part B 41 (1):27-40.
Marij van Strien (2013). The Nineteenth Century Conflict Between Mechanism and Irreversibility. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (3):191-205.
Charlotte Werndl & Roman Frigg (2015). Reconceptualising Equilibrium in Boltzmannian Statistical Mechanics and Characterising its Existence. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49:19-31.

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