Thermostatistics of overdamped motion of interacting particles

TL;DR

This paper demonstrates that the overdamped motion of interacting particles at zero temperature aligns with Tsallis thermostatistics, transitioning to classical Boltzmann-Gibbs behavior at higher temperatures, with an intermediate mixed regime.

Contribution

It introduces a nonlinear Fokker-Planck framework linking overdamped particle dynamics to Tsallis thermostatistics and identifies a novel mixed entropy regime at intermediate temperatures.

Findings

At T=0, particles follow Tsallis statistics.

At high T, classical Boltzmann-Gibbs distribution is recovered.

Intermediate T leads to a mixed entropy behavior.

Abstract

We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be directly associated with Tsallis thermostatistics. For sufficiently high values of T, the distribution of particles becomes Gaussian, so that the classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures of the thermal bath, the system displays a mixed behavior that follows a novel type of thermostatistics, where the entropy is given by a linear combination of Tsallis and Boltzmann-Gibbs entropies.