Escape from a metastable well under a time-ramped force

TL;DR

This paper investigates the thermally activated escape of an over-damped particle from a metastable well under a time-varying force, providing numerical solutions and practical approximations for the mean first passage time.

Contribution

It introduces a PDE-based method to compute MFPT and compares two approximations, one highly accurate and the other computationally simple.

Findings

Numerical solutions for MFPT under time-ramped forces.

A highly accurate approximation valid over a wide range of loading rates.

A simple, easy-to-calculate approximation for initial estimates.

Abstract

Thermally activated escape of an over-damped particle from a metastable well under the action of a time-ramped force is studied. We express the mean first passage time (MFPT) as the solution to a partial differential equation, which we solve numerically for a model case. We discuss two approximations of the MFPT, one of which works remarkably well over a wide range of loading rates, while the second is easy to calculate and can provide a valuable first estimate.