Ergodic Measure and Potential Control of Anomalous Diffusion

Bao Wen; Ming-Gen Li; Jian Liu; Jing-Dong Bao

doi:10.3390/e25071012

journal article Open Access Jun 30, 2023

Ergodic Measure and Potential Control of Anomalous Diffusion

Bao Wen Ming-Gen Li

Jian Liu

Jing-Dong Bao

Entropy Vol. 25 No. 7 pp. 1012 · MDPI AG

View at Publisher Save 10.3390/e25071012

Abstract

In statistical mechanics, the ergodic hypothesis (i.e., the long-time average is the same as the ensemble average) accompanying anomalous diffusion has become a continuous topic of research, being closely related to irreversibility and increasing entropy. While measurement time is finite for a given process, the time average of an observable quantity might be a random variable, whose distribution width narrows with time, and one wonders how long it takes for the convergence rate to become a constant. This is also the premise of ergodic establishment, because the ensemble average is always equal to the constant. We focus on the time-dependent fluctuation width for the time average of both the velocity and kinetic energy of a force-free particle described by the generalized Langevin equation, where the stationary velocity autocorrelation function is considered. Subsequently, the shortest time scale can be estimated for a system transferring from a stationary state to an effective ergodic state. Moreover, a logarithmic spatial potential is used to modulate the processes associated with free ballistic diffusion and the control of diffusion, as well as the minimal realization of the whole power-law regime. The results presented suggest that non-ergodicity mimics the sparseness of the medium and reveals the unique role of logarithmic potential in modulating diffusion behavior.

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Citations

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References

Details

Published: Jun 30, 2023
Vol/Issue: 25(7)
Pages: 1012
License: View

Authors

B

Bao Wen

Institutes of Science and Development, Chinese Academy of Sciences, Beijing 100190, China; School of Public Policy and Management, University of Chinese Academy of Sciences, Beijing 100049, China

M

Ming-Gen Li

Department of Physics, Beijing Normal University, Beijing 100875, China

J

Jian Liu

Department of Physics, Beijing Technology and Business University, Beijing 100048, China

J

Jing-Dong Bao

Department of Physics, Beijing Normal University, Beijing 100875, China

Funding

National Natural Science Foundation of China Award: 11735005

Cite This Article

Bao Wen, Ming-Gen Li, Jian Liu, et al. (2023). Ergodic Measure and Potential Control of Anomalous Diffusion. Entropy, 25(7), 1012. https://doi.org/10.3390/e25071012

Ergodic Measure and Potential Control of Anomalous Diffusion

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