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Nonlocal stationary probability distributions and escape rates for an active Ornstein-Uhlenbeck particle

We evaluate the steady-state distribution and escape rate for an Active Ornstein-Uhlenbeck Particle (AOUP) using methods from the theory of large deviations. The calculation is carried out both for small and large memory times of the active force in one-dimension. We compare our results to those obtained in the literature about colored noise processes, and we emphasize their relevance for the field of active matter. In particular, we stress that contrary to equilibrium particles, the invariant measure of such an active particle is a non-local function of the potential. This fact has many interesting consequences, which we illustrate through two phenomena. First, active particles in the presence of an asymmetric barrier tend to accumulate on one side of the potential -a ratchet effect that was missing is previous treatments. Second, an active particle can escape over a deep metastable state without spending any time at its bottom.