Fluctuations of thermal variables investigated by cross-correlation function.

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.