Europhys. Lett.
Volume 75, Number 1, July 2006
Page(s) 15 - 21
Section General
Published online 26 May 2006
Europhys. Lett., 75 (1), pp. 15-21 (2006)
DOI: 10.1209/epl/i2006-10072-2

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 $\lambda^2=m/M$, where m and M are the masses of a bath molecule and a Brownian particle, respectively. We discuss the extension to order $\lambda^4$ 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 $\lambda^4$.

05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.20.-y - Classical statistical mechanics.

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