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Thermostats: Analysis and application.

Gary P. Morriss1, Carl P. Dettmann

  • 1School of Physics, University of New South Wales, Sydney 2052 NSW, Australia.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
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This study reviews Gaussian isokinetic and isoenergetic thermostats, developing the Nose-Hoover thermostat for canonical ensemble simulations. It proves the conjugate pairing rule for nonequilibrium systems and non-negative conductivity in the Lorentz gas.

Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Nonlinear Dynamics

Background:

  • Deterministic thermostats are crucial for simulating physical systems under specific ensembles.
  • Gauss' principle of least constraint provides a foundation for thermostat development.
  • Understanding nonequilibrium systems requires robust simulation methods.

Purpose of the Study:

  • To review Gaussian isokinetic and isoenergetic thermostats historically.
  • To develop the Nose-Hoover thermostat for canonical ensemble simulations.
  • To investigate Lyapunov exponents, conjugate pairing rules, and Hamiltonian formulations in deterministic thermostat systems.

Main Methods:

  • Historical review of deterministic thermostat algorithms.
  • Development of the Nose-Hoover thermostat.

Related Experiment Videos

  • Mathematical proof of the conjugate pairing rule for potential-derived forces in nonequilibrium systems.
  • Application of periodic orbit expansion methods to the Lorentz gas model.

    • Main Results:

    • Justification of thermostats using Gauss' principle of least constraint.
    • Demonstration of Lyapunov exponents satisfying the conjugate pairing rule for certain model systems.
    • Establishment of a generalized symplectic structure and Hamiltonian formulation.
    • Proof of non-negative conductivity in the nonequilibrium Lorentz gas.

    Conclusions:

    • Deterministic thermostats, including the Nose-Hoover thermostat, are validated through theoretical frameworks like Gauss' principle.
    • The conjugate pairing rule and Hamiltonian formulations are applicable to nonequilibrium systems.
    • The study provides insights into the behavior of the Lorentz gas and its conductivity.