A Generalized Hamiltonian-based Algorithm for Rigorous Equilibrium Molecular Dynamics Simulation in the Canonical Ensemble
In this work, we employ a Hamiltonian-based procedure to derive a generalized Nosé–Hoover thermostat, which generates rigorous trajectories, corresponding to the canonical ensemble, in the absence or presence of external forces. Specifically, we prove that rigorous trajectories are generated regardless of whether the total linear momentum of the system is zero, constant, or time-dependent. Through the use of peculiar and center-of-mass coordinates, we develop a thermostat that is consistent with the definition of temperature through the equipartition theorem. The generalized algorithm reduces to the conventional Nosé–Hoover thermostat under the constraints that (i) the external forces are absent and (ii) the total linear momentum is zero. We show that the generalized algorithm satisfies the two criteria for rigor (Hamiltonian and non-Hamiltonian) that exist in the literature. Finally, we provide some numerical examples demonstrating the success of the generalized algorithm.
David J. Keffer, Chunggi Baig, Parag Adhangale, Brian J. Edwards. (2009). A generalized Hamiltonian-based algorithm for rigorous equilibrium molecular dynamics simulation in the canonical ensemble. Journal of Non-Newtonian Fluid Mechanics, Volume 152, Issues 1-3, 4th International workshop on Nonequilibrium Theromdynamics and Complex Fluids, Pages 129-139, ISSN 0377-0257, DOI: 10.1016/j.jnnfm.2007.10.004. (http://www.sciencedirect.com/science/article/B6TGV-4PX7B31-1/2/c51d72e9fc448d46171491539d904027)