Stationary shear flow in boundary driven Hamiltonian systems

We investigate stationary nonequilibrium states of particles moving according to Hamiltonian dynamics with Maxwell demon reflection rules at the walls. These rules simulate, in an energy but not phase space volume conserving way, moving boundaries. The resulting dynamics may or may not be time reversible. In either case the average rates of phase space volume contraction and macroscopic entropy production are shown to be equal for stationary hydrodynamic shear flows, i.e., when the velocity distribution of particles incident on the walls is a local Maxwellian. Molecular dynamic simulations of hard disks in a channel produce a steady shear flow with the predicted behavior.