Does a Brownian particle equilibrate?

Abstract

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 ${\lambda }^4$.

7 pages

Cited by in corpus (1)

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