Diffusivity dependence of the transition path ensemble

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-tointermediate 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.

Symmetries and Zero Modes in Sample Path Large Deviations

“…With some notable exceptions such as [26][27][28], however, most of the work for general irreversible systems and extreme events has focused only on exponential asymptotics using the large deviation minimizers themselves, solution to a deterministic optimization problem. As an additional, concrete motivation to go beyond such rough estimates in practical applications, it has been pointed out very recently that for assessing the relative importance of different instantonic transition paths, knowledge of the LDT prefactor at leading order may be vital even at comparably small noise strengths [29]. In the last year, there has been a lot of activity to provide generic numerical tools that also allow for the computation of the leading order term of the large deviation prefactor for the statistics of final time observables of small noise ordinary SDEs using symmetric Riccati matrix differential equations, either forward or backward in time [30][31][32][33].…”