Nonequilibrium Time Reversibility with Maps and Walks.

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt's and Zermélo's paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the Second Law of Thermodynamics (Loschmidt's) as well as in the time (Zermélo's, illustrating Poincaré recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems.

From hard spheres and cubes to nonequilibrium maps with thirty-some years of thermostatted molecular dynamics.

This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it developed from the National Laboratories' work to the worldwide explosion of computation of today. We contrast the past and present in atomistic simulations, emphasizing those simple models that best achieve reproducibility and promote understanding.

Heat conduction, and the lack thereof, in time-reversible dynamical systems: generalized Nosé-Hoover oscillators with a temperature gradient.

We use nonequilibrium molecular dynamics to analyze and illustrate the qualitative differences between the one-thermostat and two-thermostat versions of equilibrium and nonequilibrium (heat-conducting) harmonic oscillators. Conservative nonconducting regions can coexist with dissipative heat conducting regions in phase space with exactly the same imposed temperature field.

Time-reversal symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium.

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a simple model representing a harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the associated local Lyapunov exponents.

Smooth-particle boundary conditions.

We study the relative usefulness of static and dynamic boundary conditions as a function of system dimensionality. In one space dimension, dynamic boundaries, with the temperatures and velocities of external mirror-image boundary particles linked directly to temperatures and velocities of interior particles, perform qualitatively better than the simpler static-mirror-image boundary condition with fixed boundary temperatures and velocities. In one space dimension, the Euler-Maclaurin sum formula shows that heat-flux errors with dynamic temperature boundaries vary as h(-4), where h is the range of the smooth-particle weight function w(r View Article and Find Full Text PDF

Thermal heat reservoirs via Gauss' principle of least constraint; Dissipation, chaos, and phase-space dimensionality loss in one-dimensional chains.

We use Gauss' principle of least constraint to impose different kinetic temperatures on the two halves of a periodic one-dimensional chain. The thermodynamic result is heat flow, as predicted by the Second Law of Thermodynamics. The statistical-mechanical result can be either a phase-space limit cycle or a strange attractor, depending on the chain length and the size of the temperature difference.

Fractal dimension of steady nonequilibrium flows.

The Kaplan-Yorke information dimension of phase-space attractors for two kinds of steady nonequilibrium many-body flows is evaluated. In both cases a set of Newtonian particles is considered which interacts with boundary particles. Time-averaged boundary temperatures are imposed by Nose-Hoover thermostat forces.

Heat transfer between two degrees of freedom.

A particularly simple chaotic nonequilibrium open system with two Cartesian degrees of freedom, characterized by two distinct temperatures T(x) and T(y), is introduced. The two temperatures are maintained by Nose-Hoover canonical-ensemble thermostats. Both the equilibrium (no net heat transfer) and nonequilibrium (dissipative) Lyapunov spectra are characterized for this simple system.