N. Chernov and J. L. Lebowitz
Stationary Nonequilibrium States in Boundary Driven Hamiltonian
Systems: Shear Flow
(100K, LaTeX)
ABSTRACT. We investigate stationary nonequilibrium states of systems of particles
moving according to Hamiltonian dynamics with specified potentials. The
systems are driven away from equilibrium by Maxwell demon ``reflection
rules'' at the walls. These deterministic rules conserve energy but not
phase space volume, and the resulting global dynamics may or may not be
time reversible (or even invertible). Using rules designed to simulate
moving walls we can obtain a stationary shear flow. Assuming that for
macroscopic systems this flow satisfies the Navier-Stokes equations, we
compare the hydrodynamic entropy production with the average rate of phase
space volume compression. We find that they are equal {\it when} the
velocity distribution of particles incident on the walls is a local
Maxwellian. An argument for a general equality of this kind, based on the
assumption of local thermodynamic equilibrium, is given. Molecular dynamic
simulations of hard disks in a channel produce a steady shear flow with the
predicted behavior.