Long-time convergence of an Adaptive Biasing Force method

Tony Lelièvre (1) , Felix Otto (2) , Mathias Rousset (1) , Gabriel Stoltz (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 Instutute for Applied Mathematics [Bonn]

We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear stochastic differential equation, where the drift depends on conditional expectations of some functionals of the process. We use entropy techniques to prove exponential convergence to the stationary state.

Mots clés: non-linear Fokker-Planck equation; long-time behaviour; entropy techniques; Adaptive Biasing Force; metadynamics

Domaines: Equations aux dérivées partielles [math.AP]; Physique Numérique [physics.comp-ph]; Mécanique statistique [cond-mat.stat-mech]

Tony Lelièvre, Felix Otto, Mathias Rousset, Gabriel Stoltz. Long-time convergence of an Adaptive Biasing Force method. 2007. ⟨hal-00153946⟩