On the Hill relation and the mean reaction time for metastable processes

We illustrate how the Hill relation and the notion of quasi-stationary distribution can be used to analyse the biasing error introduced by many numerical procedures that have been proposed in the literature, in particular in molecular dynamics, to compute mean reaction times between metastable states for Markov processes. The theoretical findings are illustrated on various examples demonstrating the sharpness of the biasing error analysis as well as the applicability of our study to elliptic diffusions.(c) 2022 Published by Elsevier B.V.

Automated summary

We show how the Hill relation and the concept of quasi-stationary distribution can be applied to analyze biasing errors in various numerical procedures used in molecular dynamics to compute mean reaction times between metastable states for Markov processes. Theoretical findings are demonstrated on different examples, highlighting the precision of biasing error analysis and the applicability of our study to elliptic diffusions.