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Chaos and irreversibility in simple model systems.

Wm. G. Hoover1, Harald A. Posch

  • 1Department of Applied Science, University of California at Davis/Livermore and Lawrence Livermore National Laboratory, Livermore, California 94551-7808.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary

This study reveals a multifractal connection between chaotic mechanics and thermodynamic irreversibility. It demonstrates how conservative systems can exhibit dissipative behavior through scaling, linking microscopic and macroscopic properties.

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Area of Science:

  • Statistical Mechanics
  • Chaos Theory
  • Non-equilibrium Thermodynamics

Background:

  • Thermodynamic irreversibility is a macroscopic phenomenon.
  • Chaotic mechanics describes the time evolution of dynamical systems.
  • Understanding the link between microscopic dynamics and macroscopic thermodynamics is crucial.

Purpose of the Study:

  • To illustrate the multifractal link between chaotic time-reversible mechanics and thermodynamic irreversibility.
  • To explore analogs of dissipation in conservative systems.
  • To connect microscopic Lyapunov spectra with macroscopic dissipation.

Main Methods:

  • Analysis of three chaotic model systems: Baker Map, Galton Board, and many-body color conductivity.
  • Scaling of time, momenta, and driving forces.

Related Experiment Videos

  • Examination of Lyapunov spectra.

    • Main Results:

    • Demonstrated multifractal links between chaotic mechanics and thermodynamic irreversibility.
    • Showcased dissipative nature analogs in conservative Hamiltonian and Lagrangian mechanics via scaling.
    • Established connections between microscopic nonequilibrium Lyapunov spectra and macroscopic thermodynamic dissipation.

    Conclusions:

    • The multifractal framework provides a bridge between reversible microscopic dynamics and irreversible macroscopic thermodynamics.
    • Scaling principles can induce apparent dissipation in conservative systems.
    • Lyapunov spectra offer insights into thermodynamic dissipation mechanisms.