Time-energy tradeoff in stochastic resetting using optimal control

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Goerlich, Rémi, Olsen, Kristian Stølevik, Löwen, Hartmut, Roichman, Yael
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911079173455872
author Goerlich, Rémi
Olsen, Kristian Stølevik
Löwen, Hartmut
Roichman, Yael
author_facet Goerlich, Rémi
Olsen, Kristian Stølevik
Löwen, Hartmut
Roichman, Yael
contents Stochastic resetting is a driving mechanism that is known to minimize the first passage time to reach a target, at the cost of energy expenditure. The choice of the physical implementation of each resetting event determines the tradeoff between the acceleration of the search process and its energetic cost. Here, we present an optimal transport protocol that balances the duration and the energetic cost of each resetting event. This protocol drives a harmonically trapped Brownian particle between two equilibrium states within a finite time and with minimal energetic cost. An explicit comparison with other types of finite-time protocols further shows its specific thermodynamic properties. Its cost is both a lower bound on the cost of unoptimized shortcut protocols and an upper bound on the cost of optimal protocols which do not ensure final equilibrium. When applying the optimal transport protocol to implement stochastic resetting, a single lower time-energy bound is reached: this protocol allows to reach the best tradeoff between energetic cost and search time.
format Preprint
id arxiv_https___arxiv_org_abs_2507_19387
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Time-energy tradeoff in stochastic resetting using optimal control
Goerlich, Rémi
Olsen, Kristian Stølevik
Löwen, Hartmut
Roichman, Yael
Statistical Mechanics
Soft Condensed Matter
Stochastic resetting is a driving mechanism that is known to minimize the first passage time to reach a target, at the cost of energy expenditure. The choice of the physical implementation of each resetting event determines the tradeoff between the acceleration of the search process and its energetic cost. Here, we present an optimal transport protocol that balances the duration and the energetic cost of each resetting event. This protocol drives a harmonically trapped Brownian particle between two equilibrium states within a finite time and with minimal energetic cost. An explicit comparison with other types of finite-time protocols further shows its specific thermodynamic properties. Its cost is both a lower bound on the cost of unoptimized shortcut protocols and an upper bound on the cost of optimal protocols which do not ensure final equilibrium. When applying the optimal transport protocol to implement stochastic resetting, a single lower time-energy bound is reached: this protocol allows to reach the best tradeoff between energetic cost and search time.
title Time-energy tradeoff in stochastic resetting using optimal control
topic Statistical Mechanics
Soft Condensed Matter
url https://arxiv.org/abs/2507.19387