Stochastic processes with nonlinear dissipation: Brownian motion in Oseen's approximation

J.J. Hermans

Physica A: Statistical Mechanics and its Applications, 1981, vol. 109, issue 1, 293-304

Abstract: The random force on a Brownian particle derives from the fluctuating stresses in the liquid in which it is immersed. In earlier work by Zwanzig this was used to prove the fluctuation-dissipation theorem for a particle in a Stokes liquid. The calculation is extended to liquids that obey Oseen's hydrodynamic equations, which imply that the frictional force on the particle is a nonlinear function of its velocity. The result obtained proves the validity of the Langevin equation with Oseen's nonlinear friction, the random force being a function of the particle velocity. On the basis of this Langevin equation the Fokker-Planck equation for the velocity distribution is constructed and it is shown that this leads to Maxwell's velocity distribution.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:109:y:1981:i:1:p:293-304

DOI: 10.1016/0378-4371(81)90051-0

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