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arXiv · 2002.01319

Kinetics of rare events for non-Markovian stationary processes and application to polymer dynamics

Nicolas Levernier·Olivier Bénichou·Raphaël Voituriez·Thomas Guérin
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Abstract

How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited -- typically because of a high energy cost ? This question generally amounts to the determination of the first-passage time statistics to a target zone in phase space with lower occupation probability. Here, we present an analytical method to determine the mean first-passage time of a generic non-Markovian random walker to a rarely visited threshold, which goes beyond existing weak-noise theories. We apply our method to polymer systems, to determine (i) the first time for a flexible polymer to reach a large extension, and (ii) the first closure time of a stiff inextensible wormlike chain. Our results are in excellent agreement with numerical simulations and provide explicit asymptotic laws for the mean first-passage times to rarely visited configurations.

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Nicolas Levernier, Olivier Bénichou, Raphaël Voituriez, Thomas Guérin. 2020-02-04. Kinetics of rare events for non-Markovian stationary processes and application to polymer dynamics. https://doi.org/10.1103/physrevresearch.2.012057

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