# Aspects of Nos\'e and Nos\'e-Hoover Dynamics Elucidated

@article{Hoover2019AspectsON, title={Aspects of Nos\'e and Nos\'e-Hoover Dynamics Elucidated}, author={Wm. G. Hoover and Carol Griswold Hoover}, journal={arXiv: Statistical Mechanics}, year={2019} }

Some paradoxical aspects of the Nose and Nose-Hoover dynamics of 1984 and Dettmann's dynamics of 1996 are elucidated. Phase-space descriptions of thermostated harmonic oscillator dynamics can be simultaneously expanding, incompressible, or contracting, as is described here by a variety of three- and four-dimensional phase-space models. These findings illustrate some surprising consequences when Liouville's continuity equation is applied to Hamiltonian flows.

## References

SHOWING 1-10 OF 12 REFERENCES

### Global analysis of a generalized Nosé–Hoover oscillator

- MathematicsJournal of Mathematical Analysis and Applications
- 2018

### Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics

- Mathematics
- 1997

The Nose Hamiltonian is adapted, leading to a derivation of the Nose-Hoover equations of motion which does not involve time transformations, and in which the degree of freedom corresponding to the…

### Canonical dynamics of the Nosé oscillator: Stability, order, and chaos.

- PhysicsPhysical review. A, General physics
- 1986

The Nose oscillator is a borderline case, not sufficiently chaotic for a fully statistical description, and it is suggested that the behavior of only slightly more complicated systems is considerably simpler and in accord with statistical mechanics.

### The Coexistence of Invariant Tori and Topological Horseshoe in a Generalized Nosé-Hoover Oscillator

- MathematicsInt. J. Bifurc. Chaos
- 2017

Horseshoe chaos can be demonstrated by applying the topological horseshoe theory to a Poincare map defined in a proper cross-section, which further shows the coexistence of infinitely stable periodic trajectories and infinite saddle periodic trajectoryories.

### Canonical dynamics: Equilibrium phase-space distributions.

- PhysicsPhysical review. A, General physics
- 1985

The dynamical steady-state probability density is found in an extended phase space with variables x, p/sub x/, V, epsilon-dot, and zeta, where the x are reduced distances and the two variables epsilus-dot andZeta act as thermodynamic friction coefficients.

### A unified formulation of the constant temperature molecular dynamics methods

- Physics, Chemistry
- 1984

Three recently proposed constant temperature molecular dynamics methods by: (i) Nose (Mol. Phys., to be published); (ii) Hoover et al. [Phys. Rev. Lett. 48, 1818 (1982)], and Evans and Morriss [Chem.…

### The Equivalence of Dissipation from Gibbs' Entropy Production with Phase-Volume Loss in Ergodic Heat-Conducting Oscillators

- PhysicsInt. J. Bifurc. Chaos
- 2016

The thermostats considered here are ergodic and provide simple dynamical models, some of them with as few as three ordinary differential equations, while remaining capable of reproducing Gibbs' canonical phase-space distribution and precisely consistent with irreversible thermodynamics.

### Qualitative Analysis of the Nosé–Hoover Oscillator

- Materials ScienceQualitative Theory of Dynamical Systems
- 2020

In this paper, we analyze the qualitative behavior of the solution of the Nosé–Hoover oscillator which is a three-dimensional quadratic polynomial system. We show that every invariant set of the…

### A molecular dynamics method for simulations in the canonical ensemble

- Physics, Chemistry
- 1984

A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed.…