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Time-energy trade-off in stochastic resetting using optimal control.

Rémi Goerlich1,2, Kristian Stølevik Olsen2, Hartmut Löwen2

  • 1Tel Aviv University, Raymond & Beverly Sackler School of Chemistry, Tel Aviv 6997801, Israel.

Physical Review. E
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Summary
This summary is machine-generated.

Stochastic resetting minimizes search time but increases energy use. An optimal transport protocol balances this trade-off, achieving the best time-energy efficiency for reaching a target.

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Area of Science:

  • Physics
  • Thermodynamics
  • Statistical Mechanics

Background:

  • Stochastic resetting accelerates search processes but incurs energy costs.
  • The physical implementation of resetting dictates the balance between search speed and energy expenditure.

Purpose of the Study:

  • To introduce and analyze an optimal transport protocol for stochastic resetting.
  • To investigate the thermodynamic properties and time-energy trade-off of this protocol.

Main Methods:

  • Utilized an optimal transport protocol to drive a Brownian particle between equilibrium states.
  • Analyzed the energetic cost and duration of the resetting events.
  • Compared the protocol's performance with other finite-time protocols.

Main Results:

  • The optimal transport protocol achieves a minimal energetic cost for finite-time resetting.
  • This protocol establishes a lower bound for unoptimized protocols and an upper bound for protocols not ensuring final equilibrium.
  • The protocol demonstrates the best achievable trade-off between energy cost and search time.

Conclusions:

  • The optimal transport protocol offers a superior method for implementing stochastic resetting.
  • It provides a fundamental limit for balancing search efficiency and energy consumption in physical systems.