Time-delayed feedback turns Arrhenius escape logarithmic

Abstract

Thermal escape is governed by the Arrhenius law, where the mean escape time scales exponentially with the barrier height. We show that the non-Markovianity induced by time-delayed feedback in the confining force removes this exponential scaling. Beyond a threshold set by the curvature of the minimum, the delay destabilizes the well, and the thermal noise seeds an instability that is subsequently amplified deterministically to the boundary leading to \textit{slingshot} escape trajectories. The escape time becomes logarithmic in the barrier, its fluctuations follow a Gumbel law, and an optimal delay enables escape faster than free diffusion. Our results propose time delay as a tunable and experimentally feasible control parameter for accelerating activated processes.