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Brownian Motion from Boltzmann's Equation

1971; AIP Publishing; Volume: 14; Issue: 10 Linguagem: Inglês

10.1063/1.1693297

2163-4998

David Montgomery,

Statistical Mechanics and Entropy

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.