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

K. S. Fa; S. Pianegonda

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arXiv · 2311.17069

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

K. S. Fa·S. Pianegonda

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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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K. S. Fa, S. Pianegonda. 2023-11-24. 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. https://arxiv.org/abs/2311.17069

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