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Superexponential fluctuation relation for dichotomous work reservoir systems.

Sílvio M Duarte Queirós1

  • 1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, 150 Rua Dr. Xavier Sigaud, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil.

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Summary

This study presents a new analytical method for understanding power fluctuations in nonequilibrium systems. It reveals unique fluctuation relations for injected power, differing from standard thermal systems.

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Area of Science:

  • Non-equilibrium statistical mechanics
  • Theoretical physics
  • Complex systems

Background:

  • Understanding steady-state distributions in non-equilibrium systems is challenging.
  • Traditional models often rely on assumptions that don't apply to all systems.
  • Work reservoirs with telegraph noise present unique analytical difficulties.

Purpose of the Study:

  • To develop an analytical description for the probability density functions of dissipated and injected powers.
  • To overcome the limitations in obtaining closed-form steady-state distributions.
  • To investigate fluctuation relations in a paradigmatic non-equilibrium damped system.

Main Methods:

  • Analytical description of probability density functions.
  • Modeling the work reservoir using telegraph noise.
  • Analysis of injected and dissipated power fluctuations.

Main Results:

  • A superexponential fluctuation relation for injected power was determined, surpassing even asymptotically exponential behavior.
  • In the white-noise limit, the relation converges to the standard exponential formula for thermal systems.
  • The distribution of injected power in this system differs significantly from thermal systems.
  • A Gaussian distribution for injected power, typical of thermal systems, was shown to be achievable only for athermal reservoirs.

Conclusions:

  • The developed analytical approach provides new insights into non-equilibrium systems.
  • The findings challenge conventional understanding by demonstrating unique fluctuation behaviors.
  • The study highlights the possibility of Gaussian power distributions in athermal systems.