Transition-path probability depends non-monotonically on memory time for non-Markovian systems

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(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(TP|x) is non-monotonic as a function of the memory time and exceeds 1/2 for long memory time. This disqualifies p(TP|x) as a criterion for reaction coordinate quality. open access Copyright (c) 2025 The author(s) Published by the EPLA under the terms of the Creative Commons Attribution 4.0 International License (CC BY). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.