Non-Markovianity increases transition path probability

2025/01/08 by Florian N. Brünig, Benjamin A. Dalton, Brünig, Florian N. +5
Biochemistry, Genetics and Molecular Biology · Decision Sciences · #Biological Physics (physics.bio-ph) #Chemical Physics (physics.chem-ph) #Diffusion and Search Dynamics #FOS: Physical sciences #Gene Regulatory Network Analysis #Probabilistic and Robust Engineering Design #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2501.04512

openalex publication_date 2025/01/08 · openalex created_date 2025/01/10 · openalex updated_date 2026/08/03

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.

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