Exit event from a metastable state and Eyring-Kramers law for the overdamped Langevin dynamics

TL;DR

This paper discusses recent theoretical results on modeling the exit event from metastable states in overdamped Langevin dynamics using a Markov jump process based on the Eyring-Kramers law, providing a rigorous justification for this approximation.

Contribution

It provides a rigorous mathematical justification for using a Markov jump process with Eyring-Kramers law to model exit events in metastable regions for overdamped Langevin dynamics.

Findings

Validation of Markov jump process approximation

Derivation of Eyring-Kramers law for exit times

Theoretical support for metastability modeling

Abstract

In molecular dynamics, several algorithms have been designed over the past few years to accelerate the exit event from a metastable region of the configuration space. Some of them are based on the fact that the exit event from a metastable region is well approximated by a Markov jump process. In this work, we present recent results on the exit event from a metastable region for the overdamped Langevin dynamics obtained in [17, 18, 49]. These results aim in particular at justifying the use of a Markov jump process parametrized by the Eyring-Kramers law to model the exit event from a metastable region.