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Thermodynamic trade-off relation for first passage time in resetting processes.

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This study explores the thermodynamic cost of resetting in target-searching processes. We found that instantaneous resetting requires infinite work, and a finite-time resetting strategy offers a better time-cost trade-off.

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Area of Science:

  • Statistical physics
  • Stochastic processes
  • Thermodynamics

Background:

  • Resetting strategies accelerate target-searching processes.
  • Previous studies assumed instantaneous resetting, neglecting thermodynamic costs.
  • Instantaneous resetting incurs infinite thermodynamic cost.

Purpose of the Study:

  • To investigate the trade-off between time and thermodynamic cost in resetting processes.
  • To analyze first passage time (FPT) and work done during finite-time resetting.
  • To derive a general time-cost trade-off relation for stochastic resetting.

Main Methods:

  • Utilizing an iterative generating function method.
  • Employing a counting functional method à la Feynman and Kac.
  • Calculating FPT and average work for resetting with a trapping potential.

Main Results:

  • Derived an explicit time-cost trade-off relation for linear trapping potentials.
  • Demonstrated that instantaneous resetting is only possible with infinite work input.
  • Showed the derived trade-off relation holds for various trapping potentials.
  • Found that fixed-time resetting improves the time-cost trade-off compared to stochastic resetting.

Conclusions:

  • Finite-time resetting offers a more realistic and thermodynamically feasible approach than instantaneous resetting.
  • The derived time-cost trade-off provides a fundamental limit for resetting processes.
  • Fixed-time resetting presents a superior strategy for optimizing search efficiency under thermodynamic constraints.