Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity

Brownian yet non-Gaussian diffusion has recently been observed in numerous biological and active matter system. The cause of the non-Gaussian distribution have been elaborately studied in the idea of a superstatistical dynamics or a diffusing diffusivity. Based on a random diffusivity model, we here focus on the ergodic property and the scatter of the amplitude of time-averaged mean-squared displacement (TAMSD). By investigating the random diffusivity model with three categories of diffusivities, including diffusivity being a random variable D, a time-dependent but uncorrelated diffusivity D(t), and a correlated stochastic process D(t), we find that ensemble-averaged TAMSDs are always normal while ensemble-averaged mean-squared displacement can be anomalous. Further, the scatter of dimensionless amplitude is completely determined by the time average of diffusivity D(t). Our results are valid for arbitrary diffusivity D(t). (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Brownian yet non-Gaussian diffusion has been observed in biological and active matter systems lately. The non-Gaussian distribution has been studied in the context of superstatistical dynamics or diffusing diffusivity. Research on a random diffusivity model shows that ensemble-averaged TAMSDs are always normal, while ensemble-averaged mean-squared displacement can be anomalous, with the scatter of dimensionless amplitude determined by the time average of diffusivity D(t).