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 τ, 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 τ is sufficiently large, equilibrium-like approximations break down in the barrier crossing region. In the model under investigation, it emerges as 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 τ, 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