Accelerated escape dynamics in non-Markovian stochastic feedback

Abstract: We study the escape dynamics of a non-Markovian stochastic process with time-averaged feedback, which we model as a one-dimensional Ornstein--Uhlenbeck process wherein the drift is modified by the empirical mean of its trajectory. This process maps onto a class of self-interacting diffusions. Using weak-noise large deviation theory, we derive the most probable escape paths and quantify their likelihood via the action functional. We compute the feedback-modified Kramers rate and its inverse, which approximates the mean escape time, and show that the feedback accelerates escape by storing finite-time fluctuations thereby lowering the effective energy barrier, and shifting the optimal escape time from infinite to finite. Although we identify alternative mechanisms, such as slingshot and ballistic escape trajectories, we find that they remain sub-optimal and hence do not accelerate escape. These results show how memory feedback reshapes rare event statistics, thereby offering a mechanism to potentially control escape dynamics.