Non-Markovianity increases transition path probability

TL;DR

This paper demonstrates that in non-Markovian systems, the transition-path probability along a reaction coordinate can surpass the Markovian limit of 1/2, challenging its use as a reaction coordinate quality measure.

Contribution

The study reveals that non-Markovian dynamics cause the transition-path probability to become non-monotonic and exceed 1/2, invalidating its role as a reaction coordinate quality criterion.

Findings

Transition-path probability exceeds 1/2 in non-Markovian dynamics.

p(TP|x) is non-monotonic with respect to memory time.

Markovian limit of 1/2 is not a universal criterion.

Abstract

Defining low-dimensional reaction coordinates is crucial for analyzing the dynamics of complex systems and for comparison with experiments. The maximal value of the transition-path probability along the reaction coordinate $x$, $p(\mathrm{TP}|x)$, is a common estimator for reaction-coordinate quality by comparing to the theoretical maximal value of 1/2 in the overdamped Markovian limit. We show by analytical arguments and simulations that for non-Markovian dynamics $p(\mathrm{TP}|x)$ is non-monotonic as a function of the memory time and exceeds 1/2 for long memory time. This disqualifies $p(\mathrm{TP}|x)$ as a criterion for reaction coordinate quality.