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

Recent progress in experimental techniques, such as single particle tracking, allows one to analyze both nonequilibrium properties and an 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 an approach to nonequilibrium. We consider an archetypal model of a 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.