Nonextensive Thermostatistics and the $H$-Theorem Revisited

TL;DR

This paper derives a new form of the $H$-theorem within Tsallis' nonextensive thermostatistics, explicitly incorporating molecular dependence without modifying Boltzmann's original assumptions, leading to different equilibrium states.

Contribution

It introduces a novel derivation of the $H$-theorem that accounts for molecular dependence, avoiding modifications to Boltzmann's molecular chaos hypothesis.

Findings

Different equilibrium velocity distributions depending on the entropic parameter

Explicit incorporation of molecular dependence in collision dynamics

Revised understanding of nonextensive thermodynamics

Abstract

In this paper we present a new derivation of the $H$-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we do not assume any modification on the functional form of Boltzmann's original "molecular chaos hypothesis". Rather, we explicitly introduce into the collision scenario, the existence of statistical dependence between the molecules before the collision has taken place, through a conditional distribution $f(\vec{v}_2|\vec{v}_1)$. In this approach, different equilibrium scenarios emerge depending on the value of the nonextensive entropic parameter.