Brownian motion: a case of temperature fluctuations

TL;DR

This paper investigates how temperature fluctuations in a medium affect the diffusion process of Brownian particles, revealing that such fluctuations lead to a nonequilibrium stationary state rather than the classical Maxwell distribution.

Contribution

It introduces a model accounting for temperature fluctuations in Brownian motion, showing the resulting stationary state deviates from thermodynamic equilibrium.

Findings

Velocity distribution differs from Maxwell distribution due to temperature fluctuations

Temperature fluctuations induce a nonequilibrium stationary state

The model provides a new perspective on Brownian motion in fluctuating environments

Abstract

A diffusion process of a Brownian particle in a medium of temperature $T$ is re-considered. We assume that temperature of the medium fluctuates around its mean value. The velocity probability distribution is obtained. It is shown that the stationary state is not a thermodynamic equilibrium state described by the Maxwell distribution. Instead a nonequilibrium state is produced by temperature fluctuations.