Stochastic transitions: Paths over higher energy barriers can dominate in the early stages

TL;DR

This paper demonstrates that in stochastic systems, early transition paths often favor higher energy barriers over lower ones due to shorter phase space distances, contrasting with long-term reaction rate predictions.

Contribution

It introduces a new perspective on transition pathways by highlighting the importance of time scale, and extends the gMAM algorithm to identify most likely paths at different times.

Findings

Early transitions can favor higher energy barriers due to shorter phase space distances.

The extended gMAM algorithm can determine most likely paths at both short and long times.

Short-time transition paths differ significantly from long-time reaction pathways.

Abstract

The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two (or more) possible pathways that the system can take, the time available for the transition to occur is crucially important. The well-known results of reaction rate theory for determining the rates of the transitions apply in the long-time limit. However, at short times, the system can instead choose to pass over higher energy barriers with much higher probability, as long as the distance to travel in phase space is shorter. We construct two simple models to illustrate this general phenomenon. We also present an extension of the gMAM algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys. {\bf 128}, 061103 (2008)] to determine the most likely path at both short and long times.