Comments on the validity of the non-stationary Generalized Langevin Equation as a coarse-grained evolution equation for microscopic stochastic dynamics

TL;DR

This paper examines the validity of the non-stationary Generalized Langevin Equation for coarse-grained dynamics, extending previous deterministic assumptions to stochastic microscopic processes, and discusses implications for molecular simulation data analysis.

Contribution

It demonstrates that the non-stationary GLE applies to stochastic microscopic dynamics, broadening its applicability in molecular simulations with stochastic thermostats or barostats.

Findings

GLE applies to stochastic microscopic dynamics

Methods for estimating GLE components are applicable to stochastic data

GLE can be used for propagating stochastic molecular simulation data

Abstract

We recently showed that the dynamics of coarse-grained observables in systems out of thermal equilibrium are governed by the non-stationary generalized Langevin equation [J. Chem. Phys. 147, 214110 (2017), J. Chem. Phys. 150, 174118 (2019)]. The derivation we presented in these two articles was based on the assumption that the dynamics of the microscopic degrees of freedom was deterministic. Here we extend the discussion to stochastic microscopic dynamics. The fact that the non-stationary Generalized Langevin Equation also holds for stochastic processes implies that methods designed to estimate the memory kernel, drift term and fluctuating force term of this equation as well as methods designed to propagate it numerically, can be applied to data obtained in molecular dynamics simulations that employ a stochastic thermostat or barostat.