First passage time for superstatistical Fokker-Planck models

TL;DR

This paper investigates the first passage time in superstatistical Fokker-Planck models, establishing a link between moments of the superstatistical parameter and FPT moments, with applications to forced Brownian particles.

Contribution

It introduces a method to relate superstatistical parameter moments to FPT moments, offering a new way to validate superstatistical models.

Findings

All moments of the superstatistical parameter correspond to FPT moments.

FPT moments depend on external forces in a predictable way.

Mean FPT for a forced Brownian particle is characterized.

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.