A hybrid approach to model reduction of Generalized Langevin Dynamics

TL;DR

This paper introduces a hybrid reduction method for the Generalized Langevin Equation, combining invariant manifold techniques and fluctuation-dissipation principles to derive simplified Markovian models that retain essential dynamics.

Contribution

It presents a novel hybrid approach for reducing non-Markovian Langevin dynamics to Markovian models using invariant manifold methods and fluctuation-dissipation considerations.

Findings

Derived reduced Markovian models from non-Markovian dynamics.

Proved the commutativity of different reduction paths.

Maintained dissipative structure through fluctuation-dissipation theorem.

Abstract

We consider a classical model of non-equilibrium statistical mechanics accounting for non-Markovian effects, which is referred to as the Generalized Langevin Equation in the literature. We derive reduced Markovian descriptions obtained through the neglection of inertial terms and/or heat bath variables. The adopted reduction scheme relies on the framework of the Invariant Manifold method, which allows to retain the slow degrees of freedom from a multiscale dynamical system. Our approach is also rooted on the Fluctuation-Dissipation Theorem, which helps preserve the proper dissipative structure of the reduced dynamics. We highlight the appropriate time scalings introduced within our procedure, and also prove the commutativity of selected reduction paths.