Discussion: Malament and Zabell on Gibbs Phase Averaging

Abstract

In their paper “Why Gibbs Phase Averages Work—The Role of Ergodic Theory” (1980), David Malament and Sandy Zabell attempt to explain why phase averaging over the microcanonical ensemble gives correct predictions for the values of thermodynamic observables, for an ergodic system at equilibrium. Their idea is to bypass the traditional use of limit theorems, by relying on a uniqueness result about the microcanonical measure—namely, that it is uniquely stationary translation-continuous. I argue that their explanation begs questions about the relationship between thermodynamic equilibrium and statistical equilibrium; I argue in addition that any account which supports their view of the relationship between these two notions of equilibrium will likely use the limit theorems in traditional ways, and thereby bypass the explanation they offer.