First-passage time for superstatistical Fokker-Planck models

Abstract

The first-passage-time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the superstatistical approach can be put in one-to-one correspondence with the moments of the FPT. For systems subjected to an additional uncorrelated external force, the same statistical information is obtained from the dependence of the FPT moments on the external force. These results provide an alternative technique for checking the validity of superstatistical models. As an example, we characterize the mean FPT for a forced Brownian particle.

Diffusion-limited reactions in dynamic heterogeneous media

“…The notable exception is the work by Jain and Sebastian [46], in which the survival probability in crowded re-arranging spherical domains was derived. While some first-passage time problems and related reaction kinetics in static disordered media have been addressed [11,13,23,[47][48][49], most former studies were focused on the mean FPT and reaction rates.…”