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Optimal transitions between nonequilibrium steady states.

Samuel Monter1, Sarah A M Loos2,3, Clemens Bechinger1

  • 1Department of Physics, University of Konstanz, Konstanz 78457, Germany.

Proceedings of the National Academy of Sciences of the United States of America
|September 15, 2025
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Summary
This summary is machine-generated.

Optimal control strategies minimize thermodynamic work for finite-time transitions between nonequilibrium steady states (NESS) in microscale systems. Matching environmental response is key for optimal control in complex, memory-filled fluids.

Keywords:
microscopic systemsnonequilibrium steady statesoptimal controlviscoelastic fluids

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Optimal control of microscale processes is crucial for energy-efficient nanomachines.
  • Many real-world processes occur far from equilibrium, where memory effects are significant.
  • Previous research focused on equilibrium transitions, leaving nonequilibrium regimes underexplored.

Purpose of the Study:

  • To investigate optimal control strategies for finite-time transitions between nonequilibrium steady states (NESS).
  • To explore the role of memory in optimal control within viscous and viscoelastic environments.
  • To identify protocols minimizing thermodynamic work during NESS transitions.

Main Methods:

  • Combined experimental, theoretical, and computational approaches.
  • Studied the transition of a colloidal particle in an optical trap.
  • Analyzed control protocols in different fluid environments (viscous and viscoelastic).

Main Results:

  • Identified optimal control protocols that minimize thermodynamic work for NESS transitions.
  • Demonstrated that optimal protocols balance energy extraction and dissipation minimization.
  • Found that matching the environmental time response is crucial for optimal control in memory-laden systems.

Conclusions:

  • Optimal control strategies are essential for efficient finite-time processes in complex, nonequilibrium environments.
  • Memory effects significantly influence optimal control, requiring protocols to adapt to environmental dynamics.
  • Findings provide insights for designing control strategies in nanomachines and biological systems.