Ergodicity of Thermostat Family of Nos\'e--Hoover type

Nos\'e's pioneering 1984 work inspired a variety of time-reversible deterministic thermostats. Though several groups have developed successful doubly-thermostated models, single-thermostat models have failed to generate Gibbs' canonical distribution for the one-dimensional harmonic oscillator. Sergi and Ferrario's 2001 doubly-thermostated model, claimed to be ergodic, has a singly-thermostated version. Though neither of these models is ergodic this work has suggested a succes...

We investigate the ergodicity and "hot solvent/cold solute" problems in molecular dynamics simulations. While the kinetic moments and the stimulated Nos\'e--Hoover methods improve the ergodicity of a harmonic-oscillator system, both methods exhibit the "hot solvent/cold solute" problem in a binary liquid system. These results show that the devices to improve the ergodicity do not resolve the "hot solvent/cold solute" problem.

A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate t...

Usual approach to investigate the statistical properties of deterministically thermostated systems is to analyze the regime of the system motion. In this work the cumulant analysis is used to study the properties of the stationary probability distribution function of the deterministically thermostated harmonic oscillators. This approach shifts attention from the investigation of the geometrical properties of solutions of the systems to the studying a probabilistic measure. Th...

We compare simulations performed using the Nos\'e-Hoover and the Langevin thermostats with the Hamiltonian dynamics of a long-range interacting system in contact with a reservoir. We find that while the statistical mechanics equilibrium properties of the system are recovered by all the different methods, the Nos\'e-Hoover and the Langevin thermostats fail in reproducing the nonequilibrium behavior of such Hamiltonian.

A Langevin equation with state-dependent random force is considered. When the Helmholtz free energy is a nonincreasing function of time (the H-theorem), a generalized Einstein relation is obtained. A stochastic process of the Nos\'e--Hoover method is discussed on the basis of the Markovian approximation. It is found that the generalized Einstein relation holds for the Fokker--Planck equation associated with the stochastic Nos\'e--Hoover equation. The present result indicates ...

The Nos\'e-Hoover dynamics for isothermal-isobaric (NPT) computer simulations do not generate the appropriate partition function for ergodic systems. The present paper points out that this can be corrected with a simple addition of a constant term to only one of the equations of motion. The solution proposed is much simpler than previous modifications done towards the same goal. The present modification is motivated by the work virial theorem, which has been derived for the s...

The widely used Nose-Hoover chain (NHC) thermostat in molecular dynamics simulations is generally believed to impart the canonical distribution as well as quasi- (i.e., space filling) ergodicity on the thermostatted physical system (PS). Working with the standard single harmonic oscillator, we prove analytically that the two chain Nose-Hoover thermostat with unequal thermostat masses approach the standard Nose-Hoover dynamics and hence the PS loses its canonical and quasi-erg...

The Gaussian isokinetic and isoenergetic thermostats of Hoover and Evans are formally equivalent as remarked by Gallavotti, Rondoni and Cohen. But outside of equilibrium the fluctuations are uncontrolled and might break the equivalence. We show that equivalence is ensured if we consider an infinite system assumed to be ergodic under space translations.

Shuichi Nos\'e opened up a new world of atomistic simulation in 1984. He formulated a Hamiltonian tailored to generate Gibbs' canonical distribution dynamically. This clever idea bridged the gap between microcanonical molecular dynamics and canonical statistical mechanics. Until then the canonical distribution was explored with Monte Carlo sampling. Nos\'e's dynamical Hamiltonian bridge requires the "ergodic" support of a space-filling structure in order to reproduce the enti...