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

Xudong Wang and Yao Chen

Physica A: Statistical Mechanics and its Applications, 2021, vol. 577, issue C

Abstract: 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).

Keywords: Random diffusivity model; Anomalous diffusion; Ergodic process; Ergodicity breaking parameter; Langevin equation; Random walk (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:577:y:2021:i:c:s0378437121003630

DOI: 10.1016/j.physa.2021.126090

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