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.
Related
- Real Electric Vehicle Lithium-Ion Battery Capacity Estimation Method Based on the Fusion Model of Discrete Arrhenius and Double Extended Kalman Filter
- What Rate Theories Compute: Chemical kinetics from Arrhenius to machine-learned potentials
- A Descriptor for Non‐Arrhenius Ion Transport Enables Design of Sulfide Superionic Conductors
- AIMS: an AI experimentalist turns uncertainty into quantum matter discovery
- Escape Rooms, Arcades, and a Grain of Salt: Five Original Games for Introductory Chemistry, Built by One Instructor with Generative AI
BibTeX
@misc{podgaetsky2026timedelayed,
title = {{Time-delayed feedback turns Arrhenius escape logarithmic}},
author = {Roy Podgaetsky and Vishwajeet Kumar and Arnab Pal and Ohad Shpielberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30624},
eprint = {2608.30624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30624},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Time-delayed feedback turns Arrhenius escape logarithmic
AU - Roy Podgaetsky
AU - Vishwajeet Kumar
AU - Arnab Pal
AU - Ohad Shpielberg
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2608.30624
UR - https://arxiv.org/abs/2608.30624
AB - 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.
ER -