The Gibbs Paradox and the Definition of Entropy in Statistical Mechanics

Abstract

This article considers the Gibbs paradox and its implications for three definitions of entropy in statistical mechanics: (i) the “classical” Boltzmann entropy (SB1); (ii) the modified Boltzmann entropy that is usually proposed in response to the paradox (SB2); and (iii) a generalized version of the latter (SB2G). It is argued that (i) notwithstanding a recent suggestion to the contrary, the paradox does imply that SB1 is not a satisfactory definition of entropy; (ii) SB2 is undermined by “second-order” versions of the paradox; and (iii) SB2G solves the paradox but is not a satisfactory definition of entropy.