The effect of memory and active forces on transition path times distributions

TL;DR

This paper derives an analytical expression for transition path time distributions in one-dimensional barrier crossing, analyzing effects of memory and active forces, revealing their impact on short and long time behaviors in stochastic dynamics.

Contribution

It provides a novel analytical expression for transition path times considering non-Markovian and active force effects, enhancing understanding of stochastic barrier crossing.

Findings

Anomalous dynamics affect short-time behavior but are rare events.

Long-time decay remains exponential, contradicting stretched exponential claims.

Active forces decrease average transition path times.

Abstract

An analytical expression is derived for the transition path time distribution for a one-dimensional particle crossing of a parabolic barrier. Two cases are analyzed: (i) A non-Markovian process described by a generalized Langevin equation with a power-law memory kernel and (ii) a Markovian process with a noise violating the fluctuation-dissipation theorem, modeling the stochastic dynamics generated by active forces. In the case (i) we show that the anomalous dynamics strongly affecting the short time behavior of the distributions, but this happens only for very rare events not influencing the overall statistics. At long times the decay is always exponential, in disagreement with a recent study suggesting a stretched exponential decay. In the case (ii) the active forces do not substantially modify the short time behavior of the distribution, but lead to an overall decrease of the average transition path time. These findings offer some novel insights, useful for the analysis of experiments of transition path times in (bio)molecular systems.