Reversible measure-preserving integrators for non-Hamiltonian systems

Area of Science:

• Computational Physics
• Statistical Mechanics
• Molecular Dynamics

Background:

• Non-Hamiltonian systems, such as thermostats, are crucial in molecular dynamics simulations.
• Existing integration methods may struggle with preserving key physical quantities like energy.
• Thermostats like Nosé-Hoover and GGMT require specialized numerical treatment.

Purpose of the Study:

• To develop a systematic method for deriving reversible measure-preserving integrators.
• To apply this method to non-Hamiltonian systems, specifically thermostats.
• To validate the accuracy and energy conservation properties of the new integrators.

Main Methods:

• Exploiting the non-Poisson bracket structure of thermostat equations of motion.
• Developing a systematic procedure for integrator derivation.
• Numerical implementation and testing on the generalized Gaussian moment thermostat (GGMT) system.

Main Results:

• A novel systematic method for deriving reversible integrators was successfully developed.
• Numerical tests on the GGMT system demonstrated accurate conservation of the thermostat energy function.
• The study analyzed position and momentum distribution functions obtained using the new integrator.

Conclusions:

• The proposed method provides a robust way to generate accurate, energy-conserving integrators for non-Hamiltonian systems.
• This work enhances the reliability of molecular dynamics simulations involving thermostats.
• The derived integrators offer improved numerical stability and accuracy for complex systems.