Peculiarities of escape kinetics in the presence of athermal noises

Stochastic evolution of various dynamic systems and reaction networks is commonly described in terms of noise assisted escape of an overdamped particle from a potential well, as devised by the paradigmatic Langevin equation in which additive Gaussian stochastic force reproduces effects of thermal fluctuations from the reservoir. When implemented for systems close to equilibrium, the approach correctly explains emergence of Boltzmann distribution for the ensemble of trajectories generated by Langevin equation and relates intensity of the noise strength to the mobility. This scenario can be further generalized to include effects of non-Gaussian, burst-like forcing modeled by L\'evy noise. In this case however, the pulsatile additive noise cannot be treated as the internal (thermal), since the relation between the strength of the friction and variance of the noise is violated. Heavy tails of L\'evy noise distributions not only facilitate escape kinetics, but more importantly, change the escape protocol by altering final stationary state to a non-Boltzmann, non-equilibrium form. As a result, contrary to the kinetics induced by a Gaussian white noise, escape rates in environments with L\'evy noise are determined not by the barrier height, but instead, by the barrier width. We further discuss consequences of simultaneous action of thermal and L\'evy noises on statistics of passage times and population of reactants in double-well potentials.

Karol Capa\la, Bart\lomiej Dybiec, Ewa Gudowska-Nowak · 2019