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 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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Deterministic dynamics
- Maxwell-demon boundary conditions: Entropy production
- Shear flow
- Space-phase volume contraction