On the Thermodynamics of the q-Particles

TL;DR

This paper derives the grand partition functions for q-particles (quons) across the full range of q, generalizing the Planck distribution and exploring thermodynamic properties like state equations and condensation phenomena.

Contribution

It provides a method to compute the grand partition function for q-particles, extending the thermodynamics of quons beyond standard cases and addressing the challenges in second quantization.

Findings

Derived grand partition functions for q-particles across q in [-1,1]

Generalized Planck distribution for quons

Discussed thermodynamic behavior and condensation phenomena

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 $q\in(0,1)$.