Transport Equation for Small Systems and Nonadditive Entropy

TL;DR

This paper derives the source term of the nonextensive transport equation using Tsallis entropy, linking nonadditivity to phase space topology, and extends statistical mechanics to small systems.

Contribution

It provides a derivation of the nonextensive transport equation's source term, connecting nonadditivity with phase space topology in small systems.

Findings

Nonadditivity arises from phase space topology.

Derived the source term for the nonextensive transport equation.

Linked nonadditivity to the structure of phase space.

Abstract

The nonadditive entropy introduced by Tsallis in 1988 has been used in different fields and generalizes the Boltzmann entropy extending the possibilities of application of the statistical methods developed in the context of Mechanics. Here we investigate one of the last points of the theory that still are under discussion: the source term of the nonextensive transport equation. Based on a simple system, we show that the nonadditivity is a direct consequence of the phase space topology, and derive the source term that leads to the nonextensive transport equation.