Approach to nonequilibrium: from anomalous to Brownian diffusion via non-Gaussianity

TL;DR

This paper investigates how a driven Brownian particle in a periodic potential approaches equilibrium, revealing non-monotonic non-Gaussian behavior and its link to transient anomalous diffusion.

Contribution

It introduces a model showing non-monotonic evolution of non-Gaussianity during the approach to equilibrium in nonequilibrium systems.

Findings

Non-monotonic evolution of excess kurtosis during relaxation.

Transient anomalous diffusion correlates with non-Gaussianity.

Long-time diffusion remains Brownian but non-Gaussian.

Abstract

Recent progress in experimental techniques such as single particle tracking allows to analyze both nonequilibrium properties and approach to equilibrium. There are examples showing that processes occurring at finite timescales are distinctly different than their equilibrium counterparts. In this work we analyze a similar problem of approach to nonequilibrium. We consider an archetypal model of nonequilibrium system consisting of a Brownian particle dwelling in a spatially periodic potential and driven by an external time-periodic force. We focus on a diffusion process and monitor its development in time. In the presented parameter regime the excess kurtosis measuring the Gaussianity of the particle displacement distribution evolves in a non-monotonic way: first it is negative (platykurtic form), next it becomes positive (leptokurtic form) and then decays to zero (mesokurtic form). Despite the latter fact diffusion in the long time limit is Brownian, yet non-Gaussian. Moreover, we discover a correlation between non-Gaussianity of the particle displacement distribution and transient anomalous diffusion behavior emerging for finite timescales.