Comment on “The Gibbs paradox and the distinguishability of identical particles,” by M. A. M. Versteegh and D. Dieks [Am. J. Phys. 79, 741–746 (2011)

Abstract

We revisit recent discussions concerning the Gibbs paradox—the apparent discrepancy between the entropy change upon mixing identical gases as evaluated from the statistical mechanics of classical distinguishable particles and macroscopic thermodynamics. Contrary to what is often stated, we show that thermodynamics does not require this entropy of mixing to be zero. A zero value follows from the implicit assumption that the identical gas particles are indistinguishable. If the identical particles are explicitly assumed to be distinguishable, thermodynamics yields the same entropy of mixing as classical statistical mechanics.