Analyses of the perturbative motion in the Coupled Nosé-Hoover equation for assessing the system parameter values

The coupled Nosé-Hoover (cNH) equation offers a physical state sampling technique employed in molecular dynamics simulations, requiring fewer iterations and using a single-replica approach. The key to enhancing sampling efficiency is the ability to dynamically fluctuate the temperature of the Nosé-Hoover thermostat according to a predefined distribution. While the global behavior of cNH dynamics has been characterized probabilistically due to the existence of an invariant measure, this study focuses on a detailed analysis of the local behavior of these dynamics. We captured the local behavior of the temperature system (TS), a distinctive feature of cNH, using the TS mass and the Hessian of the TS potential. We conducted a comprehensive analysis of the Hessian and utilized these insights to assign suitable system parameter values for the cNH method. Given that the choice of parameter values influences the convergence of the distribution, selecting them appropriately is crucial from a practical perspective. In this study, we developed a method for determining suitable parameter values and validated it numerically by applying it to model systems. Our findings provide a foundation for achieving efficient and straightforward sampling simulations.