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

References in corpus (4)

• Dynamical foundations of nonextensive statistical mechanics
• Canonical and non-canonical equilibrium distribution
• Langevin Equation for the Rayleigh model with finite-ranged interactions
• On the higher order corrections to the Fokker-Planck equation

Cited by in corpus (7)

• Anomalous spatial diffusion and multifractality in optical lattices
• Generalized Fokker-Planck equation, Brownian motion, and ergodicity
• Equilibrium states of a test particle coupled to finite size heat baths
• Transient rectification of Brownian diffusion with asymmetric initial distribution
• Exact time-average distribution for a stationary non-Markovian massive Brownian particle coupled to two heat baths
• Stochastic dynamics beyond the weak coupling limit: thermalization
• Non-Markovian quantum Brownian motion: a non-Hamiltonian approach