On the Thermodynamics of the q-Particles

Since the grand partition function Z(q) for the so-called q-particles (i.e., quons), q is an element of ( 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 is an element of [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 is an element of (0, 1).