Escape rate of transiently active Brownian particle in one dimension

Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape rate of the particle. In this paper we study the escape problem for a Brownian particle that is transiently active; the activity decreases rapidly during the escape process. Using the effective equilibrium approach we analytically calculate the escape rate, under the assumption that the particle is either completely passive or fully active when crossing the barrier. We perform numerical simulations of the escape process in one dimension and find good agreement with the theoretical predictions.