1971•The Physics of FluidsRequires access

Brownian Motion from Boltzmann's Equation

David Montgomery

Abstract

Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

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Key concepts: Boltzmann equation, Fokker–Planck equation, Brownian motion, Diffusion process, Geometric Brownian motion, Langevin equation, Physics, Boltzmann constant