# 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

### Remark on "Some simple chaotic flows"

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1995

The Nose-Hoover oscillator system is the simplest mechanical system exhibiting chaos.

### 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.…

### 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.…

### 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…