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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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Unified, Geometric Framework for Nonequilibrium Protocol Optimization.

Shriram Chennakesavalu1, Grant M Rotskoff1

  • 1Department of Chemistry, Stanford University, Stanford, California 94305, USA.

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Summary
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Minimizing heat dissipation in thermodynamic cycles is crucial. This study presents a framework for optimal control protocols that minimize energy loss during system transformations, unifying thermodynamic geometry and optimal transport.

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Area of Science:

  • Physics
  • Thermodynamics
  • Statistical Mechanics

Background:

  • Minimizing dissipated heat in thermodynamic cycles is a key challenge.
  • Stochastic thermodynamics focuses on nanoscale systems and their control.

Purpose of the Study:

  • Introduce a framework for optimizing nonequilibrium control protocols.
  • Achieve minimal dissipation during system transformations between distributions.

Main Methods:

  • Developed a theoretical and computational framework for protocol optimization.
  • Utilized optimal transport theory to define paths in probability distribution space.
  • Connected thermodynamic metrics to optimal transport objective functions.

Main Results:

  • Protocols were designed to optimally transport systems, minimizing dissipative cost.
  • Demonstrated a unified geometric perspective linking thermodynamic metrics and optimal transport.
  • Showcased the robustness of the control protocol optimization beyond linear response.

Conclusions:

  • The proposed framework offers a unified view of thermodynamic geometries.
  • Optimized control protocols can significantly minimize energy dissipation.
  • The approach is applicable to various model systems and robust to different response regimes.