On the Thermodynamics of the q-Particles

Abstract

Since the grand partition function $Z_q$ for the so-called $q$-particles (i.e.,\ quons), $q\in (-1,1)$, cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for $q=0$, and its $q$-deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to $q\in [-1,1]$. We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e.,\ $q=0$) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor $1/n!$ in the $n$ term of the power series expansion with respect to the fugacity $z$. As an application, we briefly discuss the equations of the state for a gas of free quons or the condensation phenomenon into the ground state, also occurring for the Bose-like quons $q\in (0,1)$.

Published in Entropy

References in corpus (4)

• Diagonalizability of non homogeneous quantum Markov states and associated von Neumann algebras
• Harmonic analysis on inhomogeneous amenable networks and the Bose--Einstein condensation
• A proposal for the thermodynamics of certain open systems
• The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields

Cited by in corpus (2)

• Spectral actions for q-particles and their asymptotics
• On the Thermodynamics of Particles Obeying Monotone Statistics