Superstatistics of Brownian motion: A comparative study

TL;DR

This paper investigates how temperature fluctuations in Brownian particles lead to superstatistics behavior, linking mesoscopic thermodynamics with nonextensive statistical mechanics, and demonstrating the emergence of nonextensive effects through coarse-graining.

Contribution

It introduces a mesoscopic thermodynamics approach to derive effective probability distributions that explain superstatistics in Brownian motion, connecting local fluctuations with nonextensive statistics.

Findings

Effective probability distribution exhibits superstatistics behavior.

Long-time limit shows nonextensive statistical mechanics characteristics.

Coarse-graining induces nonextensive effects in the system.

Abstract

The dynamics of temperature fluctuations of a gas of Brownian particles in local equilibrium with a nonequilibrium heat bath, are described using an approach consistent with Boltzmann-Gibbs statistics (BG). We use mesoscopic nonequilibrium thermodynamics (MNET) to derive a Fokker-Planck equation for the probability distribution in phase space including the local intensive variables fluctuations. We contract the description to obtain an effective probability distribution (EPD) from which the mass density, van Hove's function and the dynamic structure factor of the system are obtained. The main result is to show that in the long time limit the EPD exhibits a similar behavior as the superstatistics distribution of nonextensive statistical mechanics (NESM), therfore implying that the coarse-graining procedure is responsible for the so called nonextensive effects.