Nonextensive statistics of the classical relativistic ideal gas

Investigating the canonical ensemble of a classical relativistic ideal gas in the Tsallis nonextensive framework we evaluate the specific heat in the extreme relativistic case in a closed form by directly employing the third constraint scenario. The canonical ensemble of N particles in D dimensions is well defined for the choice of the deformation parameter in the range . In the instance of a classical relativistic ideal gas with arbitrarily massive particles a perturbative scheme in the nonextensivity parameter (1−q) is developed by employing an infinite product expansion of the q-exponential, and a direct transformation of the internal energy from the second to the third constraint picture. All thermodynamic quantities may be uniformly evaluated to any desired perturbative order.