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Limited-control optimal protocols arbitrarily far from equilibrium.

Adrianne Zhong1, Michael R DeWeese2

  • 1Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA.

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Summary
This summary is machine-generated.

This study introduces exact finite-time optimal protocols for controlling thermodynamic systems with limited degrees of freedom, minimizing energy dissipation. These novel protocols outperform previous methods in simulations and potential experiments.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • Finite-time dissipation-minimizing protocols are crucial for stochastic thermodynamic systems driven far from equilibrium.
  • Previous methods often assumed full external control or relied on slow/fast driving approximations.
  • Real-world systems frequently possess limited control over their degrees of freedom.

Purpose of the Study:

  • To derive exact finite-time optimal control protocols for stochastic thermodynamic systems with limited control.
  • To develop a framework applicable beyond slow- and fast-driving approximations.
  • To demonstrate the efficacy of these protocols compared to existing methods.

Main Methods:

  • Framing the work-minimizing protocol as an optimal control problem using Fokker-Planck equation for probability density evolution.
  • Solving the equivalent Hamiltonian partial differential equations for optimal protocols.
  • Applying the framework to harmonic and anharmonic potentials (quartic and double-well).

Main Results:

  • Exact optimal protocols were derived for limited-control settings, outperforming previous methods.
  • Analytical results for harmonic potentials were reproduced.
  • Numerical protocols for anharmonic potentials demonstrated significant improvements.
  • The double-well potential exhibited near-constant mean position velocity under optimal control.
  • Non-monotonic optimal protocols were observed in specific timescale and barrier height regimes.

Conclusions:

  • The developed optimal control framework provides exact solutions for finite-time dissipation minimization in limited-control systems.
  • These findings offer a more practical approach for experimental and simulation studies of non-equilibrium thermodynamics.
  • The study highlights the potential for non-intuitive optimal control strategies in complex systems.