STATIONARY NONEQUILIBRIUM STATES IN BOUNDARY-DRIVEN HAMILTONIAN-SYSTEMS - SHEAR-FLOW

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.