# Activated escape of a self-propelled particle from a metastable state

## TL;DR

This paper derives exact escape rates for active particles from metastable states, revealing how self-propulsion and potential shape influence escape behavior and induce phase transitions.

## Contribution

It provides the first exact expressions for escape rates of active particles in arbitrary dimensions, including explicit solutions for RTPs and ABPs, and uncovers novel escape phenomena.

## Key findings

- Escape rate depends on full potential shape, not just barrier height.
- Particles can prefer higher barriers under certain conditions.
- Escape routes can switch discontinuously, causing dynamical phase transitions.

## Abstract

We study the noise-driven escape of active Brownian particles (ABPs) and run-and-tumble particles (RTPs) from confining potentials. In the small noise limit, we provide an exact expression for the escape rate in term of a variational problem in any dimension. For RTPs in one dimension, we obtain an explicit solution, including the first sub-leading correction. In two dimensions we solve the escape from a quadratic well for both RTPs and ABPs. In contrast to the equilibrium problem we find that the escape rate depends explicitly on the full shape of the potential barrier, and not only on its height. This leads to a host of unusual behaviors. For example, when a particle is trapped between two barriers it may preferentially escape over the higher one. Moreover, as the self-propulsion speed is varied, the escape route may discontinuously switch from one barrier to the other, leading to a dynamical phase transition.