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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 ofa high energy cost ? This question generally amounts to the determination ofthe first-passage time statistics to a target zone in phase space with loweroccupation probability. Here, we present an analytical method to determine themean first-passage time of a generic non-Markovian random walker to a rarelyvisited threshold, which goes beyond existing weak-noise theories. We apply ourmethod to polymer systems, to determine (i) the first time for a flexiblepolymer to reach a large extension, and (ii) the first closure time of a stiffinextensible wormlike chain. Our results are in excellent agreement withnumerical simulations and provide explicit asymptotic laws for the meanfirst-passage times to rarely visited configurations.

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