Classical statistical mechanics of identical particles and quantum effects

Abstract

The identification of the phase space ofN classical identical particles with the equivalence class of points is of crucial importance for statistical mechanics. We show that the refined phase space leads to the correct statistical mechanics for an ideal gas; moreover, Gibbs's paradox is resolved and the Third Law of Thermodynamics is recovered. The presence of both induced and stimulated transitions is shown as a consequence of the identity of the particles. Other results are the ‘quantum’ contribution to the second virial coefficient and the Bose-Einstein condensation. Photon bunching and Hanbury Brown-Twiss effect are also seen to follow from the classical model. The only element of quantum theory involved is the notion of phase cells necessary to make the entropy dimensionless. Assuming the existence of the light quantum or the phonon hypothesis we could derive the Planck distribution law for blackbody radiation or the Debye formula for specific heats respectively.