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Optimal work fluctuations for finite-time and weak processes.

Pierre Nazé1

  • 1Universidade Estadual Paulista, 14800-090, Araraquara, São Paulo, Brazil.

Physical Review. E
|December 20, 2023
PubMed
Summary

Minimizing work fluctuations optimizes irreversible work protocols. This study finds the optimal protocol for minimizing work variance in finite-time, weak driving processes, extending fluctuation-dissipation relations.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • Optimal protocols maximize usefulness by minimizing work fluctuations.
  • Previous studies focused on specific conditions for irreversible work optimization.

Purpose of the Study:

  • To determine the optimal protocol for minimizing work variance under finite-time and weak driving conditions.
  • To extend the fluctuation-dissipation relation to these non-equilibrium regimes.

Main Methods:

  • Analysis of classical and isothermal processes.
  • Application of an extended fluctuation-dissipation relation: W̄ = ΔF + βσ²_W/2.
  • Investigation of white-noise overdamped Brownian motion with an anharmonic stiffening trap.

Main Results:

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  • The optimal protocol for irreversible work is identical to the one minimizing work variance.
  • The fluctuation-dissipation relation is successfully extended to finite-time and weak driving processes.
  • Work probabilistic distribution analysis for Brownian motion deviates from Gaussian reduction in linear-response theory.

Conclusions:

  • Optimal protocols for irreversible work and work variance minimization coincide under specific conditions.
  • The extended fluctuation-dissipation relation provides a unified framework for understanding work fluctuations.
  • Non-Gaussian features are significant in the work distribution of driven Brownian systems.