**Persistent limit of an active particle in a nonconvex potential**

The effective potential approach has brought much recent progress to the theory of simple self-propelled particles. Gaussian colored noise models, in particular, allow one to systematically and explicitely map an active system onto an equilibrium one. The method, however, fails when the activity is persistent and the potential is not convex. Unfortunately, and somewhat expectedly, that is also where some the most interesting nonequilibrium physics tends to happen. I will discuss one of the simplest realizations of this situation: a single self-propelled particle in a 1D non convex potential in the persistent limit.