Broad class of nonlinear Langevin equations with drift and diffusion cofficients separable in time and space: Generalized n-moment, ergodicity, Einstein relation and fluctuations of the system

2023/11/24 by Kwok Sau Fa, Fa, K. S., Salete Pianegonda +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Statistical Mechanics (cond-mat.stat-mech) #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2311.17069

openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A wide class of nonlinear Langevin equations with drift and diffusion coefficients separable in time and space driven by the Gaussian white noise is analyzed in terms of a generalized n-moment. We show the system may present ergodic property, a key property in statistical mechanics, for space-time-dependent drift and diffusion coefficients. A generalized Einstein relation is also obtained. Besides, we show that the first two generalized moments and variance are useful to describe the drift and fluctuations of the system.

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