On the Thermodynamics of the q-Particles

Since the grand partition function [Formula: see text] for the so-called q-particles (i.e., quons), [Formula: see text] , cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for [Formula: see text] , 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 [Formula: see text]. We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., [Formula: see text]) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor [Formula: see text] 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 [Formula: see text].