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

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  • Wang, Xudong
  • Chen, Yao

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).

Suggested Citation

  • Wang, Xudong & Chen, Yao, 2021. "Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    • Handle: RePEc:eee:phsmap:v:577:y:2021:i:c:s0378437121003630
    DOI: 10.1016/j.physa.2021.126090
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    References listed on IDEAS

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    1. Li, Wenbo V., 1992. "Limit theorems for the square integral of Brownian motion and its increments," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 223-239, June.
    2. Carmine Di Rienzo & Vincenzo Piazza & Enrico Gratton & Fabio Beltram & Francesco Cardarelli, 2014. "Probing short-range protein Brownian motion in the cytoplasm of living cells," Nature Communications, Nature, vol. 5(1), pages 1-8, December.
    3. W. He & H. Song & Y. Su & L. Geng & B. J. Ackerson & H. B. Peng & P. Tong, 2016. "Dynamic heterogeneity and non-Gaussian statistics for acetylcholine receptors on live cell membrane," Nature Communications, Nature, vol. 7(1), pages 1-8, September.
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    Cited by:

    1. dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Wang, Zhenhai & Wang, Xudong, 2024. "Landscapes of random diffusivity processes in harmonic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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