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Irreversible processes at nonequilibrium steady states.

R F Fox1

  • 1School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 1979
PubMed
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A new Liapunov criterion for stability of nonequilibrium steady states is presented. This criterion uses the fluctuation-dissipation relation and a covariance matrix, differing from equilibrium methods.

Area of Science:

  • Thermodynamics
  • Non-equilibrium systems
  • Chemical kinetics

Background:

  • Stability analysis is crucial for understanding dynamic systems.
  • Liapunov stability criteria are well-established for equilibrium states.
  • Nonequilibrium steady states present unique challenges for stability analysis.

Purpose of the Study:

  • To establish a Liapunov criterion for the stability of nonequilibrium steady states.
  • To investigate the role of fluctuation-dissipation relations in this context.
  • To identify a suitable Liapunov function for nonequilibrium steady states.

Main Methods:

  • Construction of a Liapunov function from the covariance matrix of thermodynamic variables.
  • Application of the fluctuation-dissipation relation.

Related Experiment Videos

  • Comparison with excess entropy methods used for equilibrium states.

    • Main Results:

    • A Liapunov criterion for nonequilibrium steady states is demonstrated.
    • The covariance matrix, not excess entropy, forms the basis of the Liapunov function.
    • Keizer's proposed Liapunov function is validated as a correct candidate.

    Conclusions:

    • The established Liapunov criterion provides a robust method for analyzing the stability of nonequilibrium steady states.
    • The findings highlight fundamental differences between equilibrium and nonequilibrium stability analysis.
    • This work offers a significant advancement in the theoretical understanding of complex systems.