From Nose-Hoover chain to Nose-Hoover network: Design of non-Hamiltonian equations of motion for molecular-dynamics with multiple thermostats

A systematic algorithm to design multiple thermostat systems in the framework of the Nose-Hoover type non-Hamiltonian formulation is presented. Using 'non uniform' time transformations in a generalised Hamiltonian equation, we develop the non-Hamiltonian equations of motion for multiple thermostat systems having an arbitrary number of thermostats and arbitrary connections between a physical system and thermostats ('Nose-Hoover network'). We then present the algorithm to construct the Nose-Hoover network equations based on a simple diagram only. On the basis of this algorithm, recursively attached Nose-Hoover thermostats are introduced as an example of the Nose-Hoover network and its high efficiency in sampling the canonical distribution for an one-dimensional double-well system is illustrated by numerical calculations.