THE FREE QUON GAS SUFFERS GIBBS PARADOX

Abstract

We consider the statistical mechanics of systems of particles satisfying the q-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (Fermi) relations for q --> 1 (q --> -1), the partition functions of free gases are independent of q in the range -1 < q < 1. The partition functions exhibit Gibbs' paradox in the same way as a classical gas without a correction factor 1/N! for the statistical weight of the N-particle phase space; i.e., the statistical mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.