# Active escape dynamics: the effect of persistence on barrier crossing

## TL;DR

This paper investigates how persistence in active particles affects their barrier crossing behavior, revealing breakdowns of equilibrium approximations and the emergence of negative temperature regions at large activity times.

## Contribution

It introduces approximate trajectory equations for large activity times that predict barrier crossing behavior of active particles, highlighting non-equilibrium effects.

## Key findings

- Breakdown of equilibrium approximations at large activity times.
- Emergence of negative temperature regions in the system.
- Approximate equations successfully predict numerical results.

## Abstract

We study a system of non-interacting active particles, propelled by colored noises, characterized by an activity time $\tau$, and confined by a double-well potential. A straightforward application of this system is the problem of barrier crossing of active particles, which has been studied only in the limit of small activity. When $\tau$ is sufficiently large, equilibrium-like approximations break down in the barrier crossing region. In the model under investigation, it emerges a sort of "negative temperature" region, and numerical simulations confirm the presence of non-convex local velocity distributions. We propose, in the limit of large $\tau$, approximate equations for the typical trajectories which successfully predict many aspects of the numerical results. The local breakdown of detailed balance and its relation with a recent definition of non-equilibrium heat exchange is also discussed.