Rapid state-recrossing kinetics in non-Markovian systems

The mean first-passage time (MFPT) is one standard measure for the reaction time in thermally activated barrier-crossing processes. While the relationship between MFPTs and phenomenological rate coefficients is known for systems that satisfy Markovian dynamics, it is not clear how to interpret MFPTs for experimental and simulation time-series data generated by non-Markovian systems. Here, we simulate a one-dimensional generalized Langevin equation (GLE) in a bistable potential and compare two related numerical methods for evaluating MFPTs: one that only incorporates information about first arrivals between subsequent states and is equivalent to calculating the waiting time, or dwell time, and one that incorporates information about all first-passages associated with a given barrier-crossing event and is therefore typically employed to enhance numerical sampling. In the Markovian limit, the two methods are equivalent. However, for significant memory times, the two methods suggest dramatically different reaction kinetics. By focusing on first-passage distributions, we systematically reveal the influence of memory-induced rapid state-recrossing on the MFPTs, which we compare to various other numerical or theoretical descriptions of reaction times. Overall, we demonstrate that it is necessary to consider full first-passage distributions, rather than just the mean barrier-crossing kinetics when analyzing non-Markovian time series data.

Qingyuan Zhou, Roland R. Netz, Benjamin A. Dalton · 2024