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 , 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 is non-monotonic as a function of the memory time and exceeds 1/2 for long memory time. This disqualifies as a criterion for reaction coordinate quality.