Related papers: Non-ergodicity of Nose-Hoover dynamics
The Nose-Hoover thermostat is a deterministic dynamical system designed for computing phase space integrals for the canonical Gibbs distribution. Newton's equations are modified by coupling an additional reservoir variable to the physical…
A simple proof and detailed analysis on the non-ergodicity for multidimensional harmonic oscillator systems with Nose-Hoover type thermostat are given. The origin of the nonergodicity is symmetries in the multidimensional target physical…
Although Nose's thermostated mechanics is formally consistent with Gibbs' canonical ensemble, the thermostated Nose-Hoover ( harmonic ) oscillator, with its mean kinetic temperature controlled, is far from ergodic. Much of its phase space…
One-variable thermostats are studied as a generalization of the Nos\'e--Hoover method which is aimed to achieve Gibbs' canonical distribution with conserving the time-reversibility. A condition for equations of motion for the system with…
We show that systems driven by an external force and described by Nose-Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed in a state of canonical…
We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a…
Thermostats are dynamic equations used to model thermodynamic variables in molecular dynamics. The applicability of thermostats is based on the ergodic hypothesis. The most commonly used thermostats are designed according to the…
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).…
Ergodicity of the systems with Nos\'e-Hoover thermostat are studied. The dynamics of the heatbath variables are investigated and they can be periodic when the system has quick oscillation. The periodic behaviour of them causes the system to…
Most deterministic schemes for controlling temperature by kinetic variables (NH thermsotat), configurational variables (BT thermostat) and all phase space variables (PB thermostat) are non-ergodic for systems with a few degrees of freedom.…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs' canonical distribution for simple ( small ) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an…
We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ: the independence of the Lyapunov spectrum…
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…
The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum…
We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nos\'e-Hoover, our algorithm is based on a non-Hamiltonian…
We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|\psi(0)\rangle=|\cdots 2020\cdots \rangle$ in the presence of a trapping potential. We…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
Aspects of the Nos\'e and Nos\'e-Hoover dynamics developed in 1983-1984 along with Dettmann's closely related dynamics of 1996, are considered. We emphasize paradoxes associated with Liouville's Theorem. Our account is pedagogical, focused…
We present a new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the micro canonical ensemble of thermodynamics. We show that under the hypothesis of ergodicity the temperature can be computed as a…