Coarse-graining of overdamped Langevin dynamics via the Mori-Zwanzig formalism

TL;DR

This paper applies the Mori-Zwanzig formalism to overdamped Langevin dynamics, deriving an evolution equation for linear observables and highlighting the significance of memory effects through numerical and asymptotic analysis.

Contribution

It introduces a novel application of the Mori-Zwanzig formalism to overdamped Langevin systems, emphasizing the role of memory effects in their dynamics.

Findings

Memory effects are crucial for accurate temporal behavior.

Derived equations facilitate approximate modeling of Langevin dynamics.

Numerical and asymptotic analysis validate the importance of memory effects.

Abstract

The Mori-Zwanzig formalism is applied to derive an equation for the evolution of linear observables of the overdamped Langevin equation. To illustrate the resulting equation and its use in deriving approximate models, a particular benchmark example is studied both numerically and via a formal asymptotic expansion. The example considered demonstrates the important of memory effects in determining the correct temporal behaviour of such systems.