Entropy of Sharp Restart
arXiv:2207.02085 · doi:10.1088/1751-8121/acb183
Abstract
Restart has the potential of expediting or impeding the completion times of general random processes. Consequently, the issue of mean-performance takes center stage: quantifying how the application of restart on a process of interest impacts its completion-time's mean. Going beyond the mean, little is known on how restart affects stochasticity measures of the completion time. This paper is the first in a duo of studies that address this knowledge gap via: a comprehensive analysis that quantifies how sharp restart -- a keystone restart protocol -- impacts the completion-time's Boltzmann-Gibbs-Shannon entropy. The analysis establishes closed-form results for sharp restart with general timers, with fast timers (high-frequency resetting), and with slow timers (low-frequency resetting). These results share a common structure: comparing the completion-time's hazard rate to a flat benchmark -- the constant hazard rate of an exponential distribution whose entropy is equal to the completion-time's entropy. In addition, using an information-geometric approach based on Kullback-Leibler distances, the analysis establishes results that determine the very existence of timers with which the application of sharp restart decreases or increases the completion-time's entropy. Our work sheds first light on the intricate interplay between restart and randomness -- as gauged by the Boltzmann-Gibbs-Shannon entropy.
References in corpus (21)
- First-passage times in complex scale-invariant media
- First Passage Under Restart
- First order transition for the optimal search time of Lévy flights with resetting
- Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
- Diffusion-limited reactions in dynamic heterogeneous media
- Leapover lengths and first passage time statistics for Lévy flights
- First passages for a search by a swarm of independent random searchers
- Stochastic Search with Poisson and Deterministic Resetting
- The inspection paradox in stochastic resetting
- Thermodynamic uncertainty relation for first-passage times on Markov chains
- Optimal thermodynamic uncertainty relation in Markov jump processes
- Optimal non-Markovian search strategies with n-step memory
- Kinetic uncertainty relation on first passage time for accumulated current
- Mitigating long queues and waiting times with service resetting
- Resetting transition is governed by an interplay between thermal and potential energy
- First hitting times to intermittent targets
- A Unified Approach to Gated Reactions on Networks
- The Heat Distribution in a Logarithm Potential
- Mean-performance of Sharp Restart II: Inequality Roadmap
- First hitting times between a run-and-tumble particle and a stochastically-gated target
- Gated reactions in discrete time and space