Analytical and simulation findings reveal non-monotonic transition-path probability behavior in non-Markovian systems, challenging traditional quality measures.
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.
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Brünig et al. (2025) studied this question.
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