Beyond the relaxation time approximation

TL;DR

This paper proposes a simplified approach to modeling the time evolution of statistical ensembles by focusing on the evolution of the Tsallis distribution's nonextensivity parameter, rather than the full distribution.

Contribution

It introduces a method to describe the dynamics of distributions within the relaxation time approximation using the evolution of a single control parameter, $q(t)$.

Findings

The distribution maintains a quasi-power Tsallis form during evolution.

The evolution of the ensemble can be effectively described by the dynamics of $q(t)$.

This approach simplifies the analysis of non-equilibrium statistical systems.

Abstract

The relaxation time approximation (RTA) is a well known method of describing the time evolution of a statistical ensemble by linking distributions of the variables of interest at different stages of their temporal evolution. We show that if all the distributions occurring in the RTA have the same functional form of a quasi-power Tsallis distribution the time evolution of which depends on the time evolution of its control parameter, nonextensivity $q(t)$, then it is more convenient to consider only the time evolution of this control parameter.