Compendium of the foundations of classical statistical physics

Uffink, Jos (2006) Compendium of the foundations of classical statistical physics.

Abstract

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.