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Related Experiment Videos

Fluctuations in nonequilibrium systems.

G Nicolis1, I Prigogine

  • 1Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium.

Proceedings of the National Academy of Sciences of the United States of America
|September 1, 1971
PubMed
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The theory of fluctuations is extended to nonlinear systems far from equilibrium. A new phase-space description is needed for chemical kinetics, revealing mechanisms for instability and generalized turbulence.

Area of Science:

  • Nonlinear dynamics
  • Chemical kinetics
  • Statistical mechanics

Background:

  • The theory of fluctuations is typically applied to systems near equilibrium.
  • Nonlinear systems far from equilibrium present unique challenges for theoretical description.
  • Existing stochastic models like the "birth and death" model may be insufficient for complex systems.

Purpose of the Study:

  • To extend the theory of fluctuations to nonlinear systems operating far from equilibrium.
  • To investigate systems with multiple, distinct time scales, such as chemically reacting mixtures.
  • To develop a more accurate theoretical framework for understanding instabilities and emergent behaviors in such systems.

Main Methods:

  • Development of a detailed phase-space description beyond traditional "birth and death" models.

Related Experiment Videos

  • Analysis of systems with two separate time scales.
  • Generalization of Einstein's equilibrium theory for thermal fluctuations.

    • Main Results:

    • The inadequacy of standard stochastic chemical kinetics models is demonstrated.
    • A mechanism for instability emergence is proposed, driven by large, macroscopic fluctuations.
    • Far from equilibrium, infinitesimal fluctuations can amplify to macroscopic levels, leading to generalized turbulence.

    Conclusions:

    • A phase-space description is crucial for accurately modeling fluctuations in nonlinear, far-from-equilibrium systems.
    • Instabilities can arise from large-scale fluctuations, while small fluctuations follow generalized equilibrium theory.
    • Systems can evolve into a state of "generalized turbulence" where macroscopic and fluctuation distinctions blur.