Possible dynamics of the Tsallis distribution from a Fokker-Planck equation (I)

TL;DR

This paper investigates the dynamics of the Tsallis distribution through a Fokker-Planck framework, concluding it only describes simple isothermal systems without friction or noise, not nonequilibrium processes.

Contribution

It demonstrates that the Tsallis distribution cannot represent nonequilibrium dynamics in Langevin systems with friction and noise, clarifying its limitations.

Findings

Tsallis distribution describes only isothermal, frictionless, noise-free systems.

No nonequilibrium dynamics can be modeled using the Tsallis distribution in the studied framework.

The current form of the Tsallis distribution is limited to equilibrium scenarios.

Abstract

The dynamical property of the Tsallis distribution is studied from a Fokker-Planck equation. For the Langevin dynamical system with an arbitrary potential function, Markovian friction and Gaussian white noise, we show that no possible nonequilibrium dynamics can use the Tsallis distribution for the statistical description. The current form of the Tsallis distribution stands for a simple isothermal situation with no friction and no noise.