Generalization of Nose and Nose-Hoover isothermal dynamics

The infinitely many possible isothermal dynamics based on Nose and Nose-Hoo ver methods are investigated. Their properties and criteria for selecting d ifferent isothermal dynamics determined by various scaling functions of the thermostat s variable involved in the generalized Nose Hamiltonian [J. Jel linek and R. S. Berry, Phys. Rev. A 38, 3069 (1988)] are tested with molecu lar dynamics simulations, and examined analytically. It is shown that time scaling is related;to the scaling of the momenta. It is demonstrated that, for practical realizations, the entire generalization of the Nose-Hoover me thod reduces to only two momentum scaling functions h and u, with a functio n v defining the "potential energy" of the thermostat. The most general for m of the generalized Nose-Hoover (GNH) equations of motion is established. It enables correct-calculations of both static and dynamic equilibrium quan tities. GNH equations with h=s(alpha), u=s(upsilon) and v similar to lns ar e studied in detail. With such a choice of the functions the extended Nose- Hoover (ENH) equations are expected to produce more chaotic phase-space dyn amics than the NH equations. This is illustrated by thermalization of a one dimensional harmonic oscillator. For a system away from equilibrium the EN H thermostat is not able to provide dynamics consistent with the target tem perature, and, thus, the GNH approach reduces to the original Nose-Hoover t hermostat. A simple modification of the ENH equations is proposed which mak es the ENH thermostat also applicable to nonequilibrium states.