Does a Brownian particle equilibrate?

Details Does a Brownian particle equilibrate? Does a Brownian particle equilibrate?

2006-06-30

arxiv.org/abs/cond-mat/0607005v1

Europhys. Lett. 75, 15 (2006)

Physics

Condensed Matter

Statistical Mechanics

7 pages

Scientific paper

10.1209/epl/i2006-10072-2

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 $\lambda^4$.

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