On Boltzmann versus Gibbs and the Equilibrium in Statistical Mechanics

Abstract

Charlotte Werndl and Roman Frigg discuss the relationship between the Boltzmannian and Gibbsian framework of statistical mechanics, addressing, in particular, the question when equilibrium values calculated in both frameworks agree. This note points out conceptual confusions that could arise from their discussion, concerning, in particular, the authors’ use of “Boltzmann equilibrium.” It also clarifies the status of the Khinchin condition for the equivalence of Boltzmannian and Gibbsian equilibrium predictions and shows that it follows, under the assumptions proposed by Werndl and Frigg, from standard arguments in probability theory.