Self-consistent thermodynamics for the Tsallis statistics in the grand canonical ensemble: Nonrelativistic hadron gas

TL;DR

This paper revisits Tsallis statistics within the grand canonical ensemble for a nonrelativistic hadron gas, establishing conditions for thermodynamic consistency and demonstrating ensemble equivalence.

Contribution

It provides a self-consistent thermodynamic framework for Tsallis statistics in the grand canonical ensemble, including analytical and numerical analysis for a hadron gas.

Findings

Tsallis statistics satisfies thermodynamic requirements in the thermodynamic limit.

Equivalence of canonical, microcanonical, and grand canonical ensembles is demonstrated.

Thermodynamic potential is homogeneous of first order in extensive variables.

Abstract

In the present paper, the Tsallis statistics in the grand canonical ensemble was reconsidered in a general form. The thermodynamic properties of the nonrelativistic ideal gas of hadrons in the grand canonical ensemble was studied numerically and analytically in a finite volume and the thermodynamic limit. It was proved that the Tsallis statistics in the grand canonical ensemble satisfies the requirements of the equilibrium thermodynamics in the thermodynamic limit if the thermodynamic potential is a homogeneous function of the first order with respect to the extensive variables of state of the system and the entropic variable $z=1/(q-1)$ is an extensive variable of state. The equivalence of canonical, microcanonical and grand canonical ensembles for the nonrelativistic ideal gas of hadrons was demonstrated.