Superstatistical Brownian motion

TL;DR

This paper explores superstatistics applied to Brownian motion in environments with fluctuating temperatures, deriving a stochastic PDE and analyzing occupation times, with applications to turbulence data.

Contribution

It introduces a superstatistical framework for Brownian motion in inhomogeneous environments and derives a stochastic PDE for the system.

Findings

Derived a stochastic PDE for superstatistical Brownian motion

Analyzed occupation times in temperature-variant environments

Applied results to turbulence time series data

Abstract

As a main example for the superstatistics approach, we study a Brownian particle moving in a d-dimensional inhomogeneous environment with macroscopic temperature fluctuations. We discuss the average occupation time of the particle in spatial cells with a given temperature. The Fokker-Planck equation for this problem becomes a stochastic partial differential equation. We illustrate our results using experimentally measured time series from hydrodynamic turbulence.