Nonextensive statistics of relativistic ideal gas

TL;DR

This paper derives the specific heat and thermodynamic properties of a relativistic ideal gas within nonextensive statistics, providing a perturbative framework for arbitrary particle masses and dimensions.

Contribution

It introduces a perturbative scheme for calculating thermodynamic quantities of a relativistic ideal gas in nonextensive statistics, extending previous models to arbitrary masses and dimensions.

Findings

Explicit expression for specific heat in the third constraint scenario.

Perturbative method for thermodynamic quantities in nonextensive relativistic gases.

Range of the deformation parameter q for well-defined ensembles.

Abstract

We obtain the specific heat in the third constraint scenario for a canonical ensemble of a nonextensive extreme relativistic ideal gas in a closed form. The canonical ensemble of N particles in D dimensions is well-defined for the choice of the deformation parameter in the range 0 < q < 1 + 1 / DN. For a relativistic ideal gas with particles of arbitrary mass 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.