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Chaos in nonequilibrium two-temperature (Tx, Ty) Nosé-Hoover cell models
Hesam Arabzadeh1, Carol Griswold Hoover2, William Graham Hoover2
1Department of Chemistry, University of Missouri, Columbia, Missouri 65211, USA.
The Journal of Chemical Physics
|December 15, 2025
Summary
This study explores chaos in a particle system with anisotropic thermostatting. Entropy production deviates from linear-response theory, showing non-Gaussian momentum statistics and time-reversible dynamics.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Chaos Theory
Background:
- The Nosé-Hoover thermostat is a common method for simulating systems at constant temperature.
- Anisotropic thermostatting allows for controlled deviations from equilibrium, enabling the study of complex dynamic behaviors.
Purpose of the Study:
- To investigate chaotic dynamics and entropy production in a two-dimensional system with anisotropic thermostatting.
- To quantify phase-space contraction and compare entropy production rates with theoretical predictions.
Main Methods:
- Simulating a two-temperature Nosé-Hoover wanderer particle in a 2D periodic cell.
- Integrating six-dimensional equations of motion and computing the complete Lyapunov spectrum.
- Analyzing entropy production rates and momentum statistics under varying thermostat anisotropy.
Main Results:
- Chaos was confirmed, with phase-space contraction quantified by the Lyapunov spectrum.
- Entropy production increased nonlinearly with thermostat anisotropy, deviating from linear-response theory.
- Non-Gaussian momentum statistics were observed under strong driving, and a linear relation between dissipation and dimensionality loss was found.
Conclusions:
- The system exhibits time-reversible dynamics despite being dissipative, serving as a model for microscopic reversibility and macroscopic entropy production.
- The observed nonlinear entropy production challenges simple linear-response expectations.
- The study provides insights into chaos and thermodynamics in non-equilibrium systems.
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