The problem of ergodicity in statistical mechanics

The aim of this paper is to consider in what sense and under what conditions ergodicity is relevant for explaining the success of statistical mechanics. We argue against those who claim that ergodicity is irrelevant to this explanation, by noting that ergodic properties play different roles in equilibrium statistical mechanics 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 definition 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.