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 (resp.\ Fermi) relations for $q\to 1$ (resp.\ $q\to -1$), 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.

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References in corpus (2)

• Coherent States of the q--Canonical Commutation Relations
• The energy operator for infinite statistics

Cited by in corpus (11)

• Kinetic model for q-deformed bosons and fermions
• Coherent States of the q--Canonical Commutation Relations
• Properties of Particles Obeying Ambiguous Statistics
• Quasiclassical Limit in q-Deformed Systems, Noncommutativity and the q-Path Integral
• The Canonical Partition Function for Quons
• Spectra of Hamiltonians with Generalized Single-Site Dynamical Disorder
• Wavelets in mathematical physics: q-oscillators
• The Energy Operator for a Model with a Multiparametric Infinite Statistics
• On the Thermodynamics of the q-Particles
• Spectral actions for q-particles and their asymptotics
• On the Thermodynamics of Particles Obeying Monotone Statistics