Analysis and Simulation of Generalized Langevin Equations with Non-Gaussian Orthogonal Forces

The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, with its specific form determined by the choice of projection formalism. We compare parameters derived from different GLE formulations using molecular dynamics simulations of butane's dihedral angle dynamics. Our analysis reveals non-Gaussian contributions of the orthogonal force in different GLEs, being most enhanced for the Mori-GLE, where all non-linearities are relegated to the orthogonal force. We establish a simulation technique that correctly accounts for non-Gaussian orthogonal forces, which is critical for accurately predicting dihedral-angle mean first-passage times. We find that the accuracy of GLE simulations depends significantly on the chosen GLE formalism; the Mori-GLE offers the most numerically robust framework for capturing the statistical observables of the dihedral angle dynamics, provided the correct non-Gaussian orthogonal force distribution is used.