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

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.