Brownian motion of molecules: a stochastic approach

TL;DR

This paper derives a Langevin equation to model molecular Brownian motion, proves the fluctuation-dissipation theorem, and analyzes correlation properties of the stochastic motion.

Contribution

It introduces a stochastic approach to molecular Brownian motion, deriving key equations and correlation characteristics from first principles.

Findings

Langevin equation for molecular motion derived

Fluctuation-dissipation theorem proved

Correlation functions of Brownian motion obtained

Abstract

A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained.