Stochastic dynamics beyond the weak coupling limit: thermalization

TL;DR

This paper explores the long-time behavior of a Brownian particle's momentum beyond weak coupling, deriving generalized fluctuation-dissipation relations that guarantee thermalization at all perturbation orders.

Contribution

It introduces a microscopic framework for analyzing stochastic dynamics beyond the weak coupling limit, extending fluctuation-dissipation relations to higher orders.

Findings

Convergence to thermal equilibrium is proven at all perturbation orders.

Generalized fluctuation-dissipation relations are established.

The structure of coupled moment equations is characterized.

Abstract

We discuss the structure and asymptotic long-time properties of coupled equations for the moments of a Brownian particle's momentum derived microscopically beyond the lowest approximation in the weak coupling parameter. Generalized fluctuation-dissipation relations are derived and shown to ensure convergence to thermal equilibrium at any order of perturbation theory.