Generalized moment expansion for Brownian relaxation processes

The generalized moment expansion has previously only been used to provide an effective algorithm for the approximation of the time dependence of observables connected with reactive Brownian processes. We extend this algorithm to describe the relaxation of observables in nonreactive processes. The wide applicability of the method is demonstrated for various examples: equilibrium correlation functions like autocorrelation functions and dynamic structure factors, particle number correlation functions monitoring diffusive redistribution, and barrier crossing problems.