Narrow escape of interacting diffusing particles

TL;DR

This paper develops a formalism using fluctuating hydrodynamics and macroscopic fluctuation theory to evaluate the non-escape probability of interacting diffusing particles, linking it to mean escape times and thermal runaway phenomena.

Contribution

It introduces a novel formalism for calculating non-escape probabilities of interacting particles, connecting narrow escape problems with chemical reactor stability.

Findings

Formalism based on fluctuating hydrodynamics and macroscopic fluctuation theory.

Connection between narrow escape of interacting particles and thermal runaway.

Provides methods to evaluate mean escape times for particle systems.

Abstract

The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism that allows us to evaluate the \emph{non-escape probability} of a gas of diffusing particles that may interact with each other. In some cases the non-escape probability allows us to evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory. We also uncover an unexpected connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.