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Related Experiment Videos

Fluctuation dissipation theorems and irreversible thermodynamics.

A J McKane1, F Vazquez

  • 1Department of Theoretical Physics, University of Manchester, Manchester M13 9PL, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
Summary

This study explores fluctuations in macroscopic systems, introducing velocity fluctuations into thermodynamic models. This approach extends irreversible thermodynamics, revealing frequency-dependent transport coefficients for systems with finite signal velocity.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • Fluctuations are fundamental in macroscopic systems governed by thermodynamics.
  • Linear irreversible thermodynamics provides a framework for analyzing these fluctuations.
  • Existing models may not fully capture dynamics in systems with finite signal propagation speeds.

Purpose of the Study:

  • To investigate the statistical properties of fluctuations in macroscopic systems.
  • To elucidate the nature of fluctuations in hyperbolic macroscopic systems with finite transmission velocities.
  • To extend the understanding of fluctuation-dissipation theorems beyond traditional frameworks.

Main Methods:

  • Reviewing fluctuations within linear irreversible thermodynamics.

Related Experiment Videos

  • Explicitly including velocity fluctuations in the second variation of entropy (delta2S).
  • Applying a similar procedure to hyperbolic macroscopic systems.
  • Reformulating the fluctuating theory to connect extended and linear irreversible thermodynamics.

    • Main Results:

    • Explicit inclusion of velocity fluctuations is necessary for accurate characterization.
    • This approach extends beyond commonly defined extended irreversible thermodynamics.
    • The fluctuation-dissipation theorem is explicitly formulated for hyperbolic systems.
    • Deterministic dynamics quantities determine the statistics of stochastic variables.
    • Real, frequency-independent transport coefficients are replaced by complex, frequency-dependent ones.

    Conclusions:

    • Velocity fluctuations play a critical role in characterizing thermodynamic fluctuations.
    • The developed theory provides a more comprehensive description of fluctuations in hyperbolic systems.
    • This work bridges the gap between linear irreversible thermodynamics and extended theories by highlighting frequency-dependent transport coefficients.