We discuss the structure and asymptotic long-time properties of coupled equations for the moments of a Brownian particle's momentum $\langle p^n\left(t\right)\rangle$ derived microscopically beyond the lowest approximation in the weak coupling parameter $\lambda$. Generalized fluctuation-dissipation relations are derived and shown to ensure convergence to thermal equilibrium to any order in $\lambda$.

• Received 11 October 2011

DOI:https://doi.org/10.1103/PhysRevE.84.061124