Does a Brownian particle equilibrate?A. V. Plyukhin
Department of Physics and Engineering Physics, University of Saskatchewan Saskatoon, SK S7N 5E2, Canada
received 5 January 2006; accepted in final form 9 May 2006
published online 26 May 2006
The conventional equations of Brownian motion can be derived from the first principles to order , where m and M are the masses of a bath molecule and a Brownian particle, respectively. We discuss the extension to order using a perturbation analysis of the Kramers-Moyal expansion. For the momentum distribution such method yields an equation whose stationary solution is inconsistent with Boltzmann-Gibbs statistics. This property originates entirely from non-Markovian corrections which are negligible in lowest order but contribute to order .
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.20.-y - Classical statistical mechanics.
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