2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130233We 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.Analysis of PDEsStatistical MechanicsComputational Physics35B40, 37M25, 60K35text