Nonextensive Kinetic Theory and H-Theorem in General Relativity

TL;DR

This paper extends nonextensive kinetic theory to general relativity, demonstrating that Tsallis entropy satisfies an H-theorem under gravity and characterizing local equilibrium with q-distributions.

Contribution

It introduces a relativistic nonextensive kinetic framework with gravitational effects and proves the validity of the H-theorem and equilibrium distributions within this setting.

Findings

Tsallis entropy satisfies H-theorem in gravitational fields.

Local equilibrium is described by extended Bose-Einstein and Fermi-Dirac q-distributions.

The entropic q-parameter is constrained to [0,2] for thermodynamic consistency.

Abstract

The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval $q \in [0,2]$. As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.