The Derivation and Approximation of Coarse-grained Dynamics from Langevin Dynamics

TL;DR

This paper derives a coarse-grained model from Langevin dynamics focusing on the memory kernel and fluctuation-dissipation theorem, introducing rational approximations that improve accuracy and computational efficiency.

Contribution

It introduces a hierarchy of rational approximations for the memory and noise terms, reducing computational cost while increasing accuracy.

Findings

Hierarchical rational approximations improve model accuracy.

Approximations eliminate the need for integral evaluation at each step.

Enhanced computational efficiency in coarse-grained Langevin models.

Abstract

We present a derivation of a coarse-grained model from the Langevin dynamics. The focus is placed on the memory kernel function and the fluctuation-dissipation theorem. Also presented is an hierarchy of approximations for the memory and random noise terms, using rational approximations in the Laplace domain. These approximations offer increasing accuracy. More importantly, they eliminate the need to evaluate the integral associated with the memory term at each time step.