The gibbs paradox and the definition of entropy in statistical mechanics

摘要

This article considers the Gibbs paradox and its implications for three definitions of entropy in statistical mechanics: (i) the "classical" Boltzmann entropy (S B1); (ii) the modified Boltzmann entropy that is usually proposed in response to the paradox (S B2); and (iii) a generalized version of the latter (S B2G). It is argued that (i) notwithstanding a recent suggestion to the contrary, the paradox does imply that S B1 is not a satisfactory definition of entropy; (ii) S B2 is undermined by "second-order" versions of the paradox; and (iii) S B2G solves the paradox but is not a satisfactory definition of entropy.