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Updated: Jun 26, 2025

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Ergodic criterion of a random diffusivity model.

Zhongshuai Zhan1, Xudong Wang1

  • 1School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China.

Physical Review. E
|May 17, 2024
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Summary
This summary is machine-generated.

Researchers developed a criterion to determine the ergodic properties of random diffusivity models. This method uses the correlation function of random diffusivity to analyze particle motion in complex systems.

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Area of Science:

  • Statistical Physics
  • Complex Systems Analysis
  • Non-Gaussian Diffusion

Background:

  • Random diffusivity explains non-Gaussian diffusion and particle motion in complex environments.
  • Understanding the ergodic properties of diffusion models is crucial for accurate analysis.
  • Existing frameworks may not fully capture the nuances of arbitrary random diffusivity.

Purpose of the Study:

  • To propose a general, quantitative criterion for determining the ergodic property of Langevin equations with arbitrary random diffusivity.
  • To establish an analytical framework for characterizing particle motion in complex environments using random diffusivity.
  • To validate the proposed criterion using established diffusivity models.

Main Methods:

  • Derivation of a general criterion based on the correlation function C(t1,t2) of random diffusivity D(t).
  • Analysis of two cases: stationary diffusivity and non-stationary diffusivity.
  • Application of the criterion to typical diffusivity models, including Brownian motion and Ornstein-Uhlenbeck processes.

Main Results:

  • A quantitative criterion for judging ergodic properties of random diffusivity models was successfully derived.
  • The criterion effectively distinguishes between different ergodic properties based on the diffusivity's correlation function.
  • The study validates the criterion by showing distinct ergodic behaviors for Brownian motion and Ornstein-Uhlenbeck processes.

Conclusions:

  • The proposed criterion provides a direct method to assess the ergodic properties of random diffusivity models.
  • The correlation function of random diffusivity is a key determinant of ergodic behavior.
  • This work offers a robust analytical tool for studying complex particle dynamics.