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

N. Levernier (1) , O. Bénichou (2) , R. Voituriez (3) , Thomas Guérin (4)

1 NCCR-Chemical Biology - Swiss National Centre for Competence in Research Programme Chemical Biology
2 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
3 LJP - Laboratoire Jean Perrin
4 LOMA - Laboratoire Ondes et Matière d'Aquitaine

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Matière Molle [cond-mat.soft]; Chimie-Physique [physics.chem-ph]

N. Levernier, O. Bénichou, R. Voituriez, Thomas Guérin. Kinetics of rare events for non-Markovian stationary processes and application to polymer dynamics. Physical Review Research, In press. ⟨hal-02466797⟩