Effective dynamics for non-reversible stochastic differential equations: a quantitative study

TL;DR

This paper develops and analyzes an effective dynamics approach for non-reversible stochastic differential equations, providing error bounds and extending coarse-graining techniques beyond reversible systems.

Contribution

It introduces a new effective dynamics framework for non-reversible systems and establishes trajectorial error bounds, advancing coarse-graining methods in this setting.

Findings

Error bounds on trajectorial differences are established.

The mean force concept remains valid in non-reversible dynamics.

The approach extends coarse-graining techniques to non-reversible systems.

Abstract

Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been devoted to coarse-graining starting from reversible systems, not much is known in the non-reversible setting. In this article, starting with a non-reversible dynamics, we introduce and study an effective dynamics which approximates the (non-closed) projected dynamics. Under fairly weak conditions on the system, we prove error bounds on the trajectorial error between the projected and the effective dynamics. In addition to extending existing results to the non-reversible setting, our error estimates also indicate that the notion of mean force motivated by this effective dynamics is a good one.