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Heat transfer between two degrees of freedom
William G. Hoover1, Errol Craig, Harald A. Posch
1Department of Applied Science, P.O. Box 808, University of California at Davis-Livermore, Livermore, California 94550Institute for Experimental Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, AustriaTheoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545National Energy Research Supercomputer Center, P.O. Box 5509, Livermore, California 94550.
Chaos (Woodbury, N.Y.)
|October 1, 1991
Summary
This study introduces a simple chaotic system with two distinct temperatures, maintained by Nose-Hoover thermostats. Researchers characterized both equilibrium and nonequilibrium Lyapunov spectra for this open system.
Area of Science:
- Statistical mechanics
- Non-equilibrium thermodynamics
- Chaos theory
Background:
- Open systems in statistical mechanics can exhibit complex behaviors.
- Understanding the dynamics of systems with distinct temperature gradients is crucial.
- Lyapunov spectra are key indicators of system stability and chaos.
Purpose of the Study:
- To introduce a simplified chaotic open system with two distinct temperatures.
- To investigate the Lyapunov spectra in both equilibrium and nonequilibrium states.
- To provide a tractable model for studying dissipative chaotic dynamics.
Main Methods:
- Development of a simple chaotic open system with two Cartesian degrees of freedom.
- Implementation of Nose-Hoover canonical-ensemble thermostats to maintain distinct temperatures T(x) and T(y).
- Characterization of Lyapunov spectra for both equilibrium and nonequilibrium conditions.
Main Results:
- Successfully introduced and characterized a simple chaotic nonequilibrium open system.
- Calculated and analyzed Lyapunov spectra for both equilibrium (no net heat transfer) and nonequilibrium (dissipative) states.
- Demonstrated the system's ability to exhibit chaotic dynamics under controlled temperature gradients.
Conclusions:
- The proposed system serves as a fundamental model for exploring chaotic phenomena in open, nonequilibrium environments.
- Characterization of Lyapunov spectra provides insights into the stability and dynamics of dissipative systems.
- This work lays the groundwork for further investigations into complex behaviors in temperature-gradient systems.