Active escape dynamics: the effect of persistence on barrier crossing

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.