Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes
- How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x) = D0|x|gamma and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify byHow different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x) = D0|x|gamma and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicitybreaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB similar to(1/r )-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.…
Author details: | Wei WangORCiD, Andrey G. CherstvyORCiDGND, Holger KantzORCiDGND, Ralf MetzlerORCiDGND, Igor M. SokolovORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.104.024105 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/34525678 |
Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
Publisher: | American Institute of Physics |
Place of publishing: | Woodbury, NY |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/08/05 |
Publication year: | 2021 |
Release date: | 2024/05/23 |
Volume: | 104 |
Issue: | 2 |
Article number: | 024105 |
Number of pages: | 27 |
Funding institution: | Humboldt University of Berlin; Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [ME 1535/7-1, ME 1535/12-1]; Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej) within an Alexander von Humboldt Polish Honorary Research Scholarship |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
5 Naturwissenschaften und Mathematik / 57 Biowissenschaften; Biologie / 570 Biowissenschaften; Biologie | |
Peer review: | Referiert |