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Updated: Apr 7, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
691
Fluctuations around equilibrium laws in ergodic continuous-time random walks.
Johannes H P Schulz1, Eli Barkai1
1Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 52900, Israel.
Summary
Occupation time statistics in random walks reveal dual scaling laws near nonergodic phases. Consistent interpretation of infinite and Lévy-stable densities resolves unphysical divergences in fluctuation analysis.
Area of Science:
- Statistical Mechanics
- Complex Systems
Background:
- Ergodic continuous-time random walks (CTRWs) are fundamental models in statistical physics.
- Understanding occupation time statistics is crucial for characterizing system dynamics and equilibrium properties.
Purpose of the Study:
- To investigate occupation time statistics in CTRWs, particularly near the nonergodic phase.
- To analyze the nature and interplay of finite-time fluctuations around the mean occupation time.
Main Methods:
- Analysis of occupation time statistics in ergodic CTRWs under thermal detailed balance.
- Examination of fluctuation distributions and scaling laws in the vicinity of the nonergodic phase.
Main Results:
- The average occupation time follows the Boltzmann-Gibbs canonical law in equilibrium.
- Close to the nonergodic phase, fluctuations exhibit dual time scaling and distribution laws: infinite density for large fluctuations and Lévy-stable density for bulk fluctuations.
- Unphysical divergences in these densities are resolved by consistent interpretation of both laws.
Conclusions:
- Canonical equilibrium laws govern not only mean occupation times but also the densities of fluctuations.
- The duality of stable and infinite densities is a ubiquitous feature of these dynamics for general physical observables.
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