Brownian-motion approach to statistical mechanics: Langevin equations, fluctuations, and timescales
arXiv:2503.01044 · doi:10.1063/5.0255687
Abstract
We briefly review the problem of Brownian motion and describe some intriguing facets. The problem is first treated in its original form as enunciated by Einstein, Langevin, and others. Then, utilizing the problem of Brownian motion as a paradigm and upon using the Langevin equation(s), we present a brief exposition of the modern areas of stochastic thermodynamics and fluctuation theorems in a manner accessible to a non-expert. This is followed by an analysis of non-Markovian Brownian dynamics via generalized Langevin equation(s) in which we particularly shed light onto its derivation, the emergence of the fluctuation-dissipation relation, and the recently-discovered effective-mass framework.
v1: Invited review in the special collection entitled '250 Years of Brownian Motion' published by Physics of Fluids; v2: This version corrects minor expository errors in Sec. (II) and fixes some typos appearing in the published version
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