On the Thermodynamics of the q -Particles.

Since the grand partition function Zq for the so-called q -particles (i.e., quons), q∈(-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∈[-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∈(0,1).