Diffusivity dependence of the transition path ensemble

TL;DR

This paper investigates the limitations of instanton approximations in describing transition pathways of stochastic systems at various temperatures, introducing an improved method that accounts for fluctuations and validating it with Monte Carlo sampling.

Contribution

It demonstrates the failure of instantons at certain temperatures and develops a fluctuation-inclusive approximation validated by numerical sampling.

Findings

Instantons can fail to capture dominant transition pathways at low-to-intermediate temperatures.

An approximation including fluctuations around instantons improves accuracy.

The method's validity range is established through comparison with Monte Carlo results.

Abstract

Transition pathways of stochastic dynamical systems are typically approximated by instantons. Here we show, using a dynamical system containing two competing pathways, that at low-to-intermediate temperatures, instantons can fail to capture the most likely transition pathways. We construct an approximation which includes fluctuations around the instanton and, by comparing with the results of an accurate and efficient path-space Monte Carlo sampling method, find this approximation to hold for a wide range of temperatures. Our work delimits the applicability of large deviation theory and provides methods to probe these limits numerically.