Thermostats: Analysis and application.

  title={Thermostats: Analysis and application.},
  author={Gary P. Morriss and Carl P. Dettmann},
  volume={8 2},
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… 

The Role of Nonconservative Interactions in the Asymptotic Limit of Thermostatted Kinetic Models

This paper is concerned with the asymptotic analysis of space-velocity dependent thermostatted kinetic frameworks which include conservative, nonconservative and stochastic operators. The

Generalized coupling to a heat bath: Extension of the Gaussian isokinetic dynamics and effect of time scaling

The Hamiltonian formulation of the Gaussian isokinetic (GIK) thermostat [C. P. Dettmann and G. P. Morriss, Phys. Rev. E 54, 2495 (1996)] is extended to generalize the coupling of a physical system to

Entropy Balance, Multibaker Maps, and the Dynamics of the Lorentz Gas

We extend and review recent results on nonequilibrium transport processes described by multibaker maps. The relation of these maps to the dynamics of the Lorentz gas is discussed. Special emphasis is

A Convergence Theorem for the Nonequilibrium States in the Discrete Thermostatted Kinetic Theory

The existence and reaching of nonequilibrium stationary states are important issues that need to be taken into account in the development of mathematical modeling frameworks for far off equilibrium

Existence of stationary solutions in kinetic models with Gaussian thermostats

The thermostatted kinetic framework has been recently proposed in [C. Bianca, Nonlinear Analysis: Real World Applications 13 (2012) 2593‐2608] for the modeling of complex systems in the applied

The Lorentz Gas: A Paradigm for Nonequilibrium Stationary States

Nonequilibrium stationary states form the building blocks of more complicated nonequilibrium systems as they define the transport coefficients appearing in the hydrodynamic equations. Recently, many

On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks

This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose

Entropy and density of states from isoenergetic nonequilibrium processes.

  • A. B. Adib
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
Two identities in statistical mechanics involving entropy differences (or ratios of densities of states) at constant energy are derived and can be conveniently used in conjunction with a scaling relation that allows one to extrapolate measurements taken at a single energy to a wide range of energy values.

Thermostating by deterministic scattering: heat and shear flow.

A recently proposed thermostating mechanism is applied to an interacting many-particle system where the bulk particles are moving according to Hamiltonian dynamics and yields well-defined nonequilibrium steady states in the range of linear response.



Hamiltonian formulation of the Gaussian isokinetic thermostat.

  • DettmannMorriss
  • Physics
    Physical 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.

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

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.

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.

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

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.

  • Hoover
  • Physics
    Physical 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

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