Ni. Chernov et Jl. Lebowitz, STATIONARY NONEQUILIBRIUM STATES IN BOUNDARY-DRIVEN HAMILTONIAN-SYSTEMS - SHEAR-FLOW, Journal of statistical physics, 86(5-6), 1997, pp. 953-990
We investigate stationary nonequilibrium states of systems of particle
s moving according to Hamiltonian dynamics with specified potentials.
The systems are driven away from equilibrium by Maxwell-demon ''reflec
tion rules'' at the: walls. These deterministic rules conserve energy
but not phase space volume, and the resulting global dynamics may or m
ay not he time reversible (or even invertible). Using rules designed t
o simulate moving walls: we can obtain a stationary shear flow. Assumi
ng that For macroscopic systems this flow satisfies the Navier-Stokes
equations, we compare the hydrodynamic entropy production with the ave
rage rate of phase-space volume compression. We find that they are equ
al when the velocity distribution of particles incident on the walls i
s 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 st
eady shear flow with the predicted behavior.