Does a Brownian particle equilibrate?
Plyukhin, A. V.
Original · EN
The conventional equations of Brownian motion can be derived from the first principles to order λ²=m/M, where m and M are the masses of a bath molecule and a Brownian particle respectively. We discuss the extension to order λ⁴ 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 λ⁴.
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