Non-Arrhenius barrier crossing dynamics of non-equilibrium non-Markovian systems

Abstract

The non-equilibrium non-Markovian barrier-crossing dynamics of a one-dimensional massive coordinate, described by the non-equilibrium version of the generalized Langevin equation with unequal random and friction relaxation times, is studied by simulations and analytical methods. Within a harmonic approximation, a general formula for the barrier-crossing time is derived which agrees favorably with simulations. Non-equilibrium random forces with a relaxation time longer than the friction relaxation time induce non-Arrhenius behavior and dramatically increase the barrier-crossing time; within the harmonic theory this corresponds to a reduced effective temperature which also modifies the spatial and velocity distributions.

First passage time statistics of non-Markovian random walker: Onsager's regression hypothesis approach

“…How long does it take for a random walker to reach a destination? Such a question on the first passage time (FPT) is relevant to a broad range of situations in science, technology and every-day life applications as encountered, for instance, in diffusion-limited reactions [1][2][3], barrier crossing [4][5][6][7], target search processes [8,9], cyclization of DNA molecule [10][11][12][13], price fluctuation in market [2] and spread of diseases [14]. Today, the concept of the FPT and its importance in the study of stochastic processes are well recognized, and theoretical methods for its computation are standardized [1,2].…”