Relativity, nonextensivity, and extended power law distributions

TL;DR

This paper extends relativistic kinetic theory by incorporating nonextensive effects, deriving a relativistic q-power law distribution that generalizes the Juttner distribution and aligns with special relativity principles.

Contribution

It provides a proof of the relativistic H-theorem with nonextensive effects and derives the relativistic q-distribution, connecting nonextensive thermodynamics with special relativity.

Findings

Relativistic q-distribution reduces to Juttner distribution in the extensive limit.

The q-parameter is constrained to [0,2] by thermodynamic principles.

The framework applies to charged gases in electromagnetic fields.

Abstract

A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics combined with a duality transformation implies that the q-parameter lies on the interval [0,2]. It is also proved that the collisional equilibrium states (null entropy source term) are described by the relativistic $q$-power law extension of the exponential Juttner distribution which reduces, in the nonrelativistic domain, to the Tsallis power law function. As a simple illustration of the basic approach, we derive the relativistic nonextensive equilibrium distribution for a dilute charged gas under the action of an electromagnetic field $F^{{\mu\nu}}$. Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the space-time ideas contained in the special relativity theory.