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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
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.
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.
- 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.