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

Tony Lelièvre (1, 2) , Dorian Le Peutrec (3) , Boris Nectoux (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS
3 LMO - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: Exit event; Metastability; Eyring-Kramers and overdamped Langevin

Domaines: Equations aux dérivées partielles [math.AP]

Tony Lelièvre, Dorian Le Peutrec, Boris Nectoux. Exit event from a metastable state and Eyring-Kramers law for the overdamped Langevin dynamics. Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017., 282, pp.331-363, 2019, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-030-15096-9_9⟩. ⟨hal-01696187v3⟩