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

2020/11/12 by Xudong Wang, Yao Chen · 17 citations
Biochemistry, Genetics and Molecular Biology · Environmental Science · Mathematics · Physics and Astronomy · #Amplitude #Brownian motion #Diffusion #Diffusion and Search Dynamics #Dimensionless quantity #Ecosystem dynamics and resilience #Ergodic theory #Ergodicity #Gaussian #Mass diffusivity #Mathematical analysis #Mathematics #Mean squared displacement #Molecular dynamics #Physics #Quantum mechanics #Statistical physics #Statistics #Stochastic process #Thermal diffusivity #Thermodynamics #Uncorrelated #cond-mat.stat-mech #stochastic dynamics and bifurcation

paper · pdf · doi:10.1016/j.physa.2021.126090

published in Physica A Statistical Mechanics and its Applications 577, 126090 (Elsevier BV)

arxiv created 2020/11/12 · openalex publication_date 2021/05/11 · arxiv updated 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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). Further, we individually investigate this 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 determined by the time average of diffusivity D(t). Our results are valid for arbitrary diffusivities.

Citations

• Anomalous diffusion in correlated continuous time random walks
• Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
• Fractional Brownian Motions, Fractional Noises and Applications
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• A fractional diffusion equation for two-point probability distributions of a continuous-time random walk
• LXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin
• Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• Tempered fractional Brownian motion
• Non-Normalizable Densities in Strong Anomalous Diffusion: Beyond the Central Limit Theorem
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• First passage statistics for diffusing diffusivity
• Lévy-walk-like Langevin dynamics
• Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity