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Does a Brownian particle equilibrate?

A. V. Plyukhin
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Abstract

The conventional equations of Brownian motion can be derived from the first principles to order $λ^2=m/M$, where $m$ and $M$ are the masses of a bath molecule and a Brownian particle respectively. We discuss the extension to order $λ^4$ 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 $λ^4$.

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A. V. Plyukhin. 2006-06-30. Does a Brownian particle equilibrate?. https://doi.org/10.1209/epl%2Fi2006-10072-2

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