Relativistic Nonextensive Thermodynamics

TL;DR

This paper develops a relativistic nonextensive thermodynamics framework based on Tsallis' statistics, deriving a Boltzmann equation, H-theorem, and thermodynamic functions for a perfect gas.

Contribution

It introduces a relativistic nonextensive thermodynamics approach using Tsallis' entropy, including a new Boltzmann transport equation and equilibrium thermodynamics.

Findings

Derived a relativistic Boltzmann equation consistent with nonextensive entropy.

Proved the H-theorem within the nonextensive relativistic context.

Obtained thermodynamic functions and equation of state for a perfect gas at equilibrium.

Abstract

Starting from the basic prescriptions of the Tsallis' nonextensive thermostatistics, i.e. generalized entropy and normalized q-expectation values, we study the relativistic nonextensive thermodynamics and derive a Boltzmann transport equation that implies the validity of the H-theorem where a local nonextensive four-entropy density is considered. Macroscopic thermodynamic functions and the equation of state for a perfect gas are derived at the equilibrium.