# Thermostats: Analysis and application.

@article{Morriss1998ThermostatsAA, title={Thermostats: Analysis and application.}, author={Gary P. Morriss and Carl P. Dettmann}, journal={Chaos}, year={1998}, volume={8 2}, pages={ 321-336 } }

Gaussian isokinetic and isoenergetic deterministic thermostats are reviewed in the correct historical context with their later justification using Gauss' principle of least constraint. The Nose-Hoover thermostat for simulating the canonical ensemble is also developed. For some model systems the Lyapunov exponents satisfy the conjugate pairing rule and a Hamiltonian formulation is obtained. We prove the conjugate pairing rule for nonequilibrium systems where the force is derivable from a…

## 94 Citations

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## References

SHOWING 1-10 OF 53 REFERENCES

### Hamiltonian formulation of the Gaussian isokinetic thermostat.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996

The usual ~Lagrangian and Hamiltonian! descriptions of classical mechanics are formulated in terms of variational principles, which allow a compact representation of the system by a single function, simplify perturbation theory, and make a connection with quantum mechanics.

### The conjugate-pairing rule for non-Hamiltonian systems.

- PhysicsChaos
- 1998

Computer simulations provide convincing evidence that the standard molecular dynamics algorithm for calculating shear viscosity violates the Conjugate Pairing Rule, and it appears that the sum of the maximal exponents is equal to the entropy production per degree of freedom.

### Nonequilibrium molecular dynamics via Gauss's principle of least constraint

- Physics
- 1983

Gauss's principle of least constraint is used to develop nonequilibrium molecular-dynamics algo rithms for systems SUbject to constraints. The treatment not only includes "nonholonomic"…

### Variational principles for thermostatted systems.

- PhysicsChaos
- 1998

A generalized Lagrangian formalism is proposed for dealing with interacting many body systems subject to time reversible friction forces and applications to Nose-Hoover and isokinetic dynamics are treated in detail.

### The nonequilibrium Lorentz gas.

- Physics, MathematicsChaos
- 1995

This work presents a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the fundamental domain of a Lorentz gas system.

### Applications of periodic orbit theory toN-particle systems

- Physics
- 1997

In recent years a number of new techniques have become available in nonequilibrium statistical mechanics, all derived from dynamical system theory, especially from the thermodynamic formalism of…

### 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.

### 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…