Long-time convergence of an Adaptive Biasing Force method

TL;DR

This paper proves the long-time convergence of an adaptive biasing force method in molecular dynamics, demonstrating exponential convergence to the stationary state using entropy techniques.

Contribution

It provides a rigorous mathematical proof of convergence for an adaptive method in molecular dynamics, which was previously lacking.

Findings

Exponential convergence to the stationary state established.

Uses entropy techniques for the proof.

Analyzes a non-linear stochastic differential equation.

Abstract

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.