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Fluctuations of thermal variables investigated by cross-correlation function.

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  • 1<a href="https://ror.org/02rx3b187">Université Grenoble Alpes</a>, CNRS, Grenoble INP, Institut NÉEL, 38000 Grenoble, France.

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This study introduces a new method to derive fluctuation formulas for systems in equilibrium using cross-correlation functions. It establishes fluctuation-dissipation relations and a general entropy production formula for thermal variables.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • Understanding thermodynamic fluctuations is crucial for characterizing systems in equilibrium.
  • Existing methods for deriving fluctuation formulas can be complex.
  • Fluctuation-dissipation relations connect microscopic properties to macroscopic response.

Purpose of the Study:

  • To develop a novel procedure for deriving fluctuation formulas for systems in equilibrium.
  • To investigate the application of cross-correlation functions for thermodynamic variables.
  • To establish general relations for entropy production and fluctuation-dissipation.

Main Methods:

  • Utilizing the cross-correlation function to analyze fluctuations in conjugate thermodynamic variables.
  • Employing the cross-correlation function between heat and temperature for thermal variables.
  • Deriving fluctuation-dissipation relations involving frequency-dependent specific heat.

Main Results:

  • A new procedure for deriving fluctuation formulas in equilibrium systems is presented.
  • The cross-correlation function is shown to be effective for thermal variables.
  • General relations for average entropy production and fluctuation-dissipation are established.

Conclusions:

  • The developed procedure offers a systematic way to study fluctuations in equilibrium.
  • The findings provide a microscopic basis for dissipation in linear response theory.
  • The results are applicable to various fluctuating thermal systems in equilibrium.