The free quon gas suffers Gibbs' paradox

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 $q\to 1$ ($q\to -1\mathrm{}$), the partition functions of free gases are independent of $q$ in the range $-1<q<\mathrm{}1\mathrm{}$. The partition functions exhibit Gibbs' paradox in the same way as a classical gas without a correction factor $\frac{1}{N}!$ 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.