Journal of Statistical Physics

, Volume 86, Issue 5–6, pp 953–990 | Cite as

Stationary nonequilibrium states in boundary-driven Hamiltonian systems: Shear flow

  • N. I. Chernov
  • J. L. Lebowitz


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 equalwhen 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.

Key Words

Shear flow deterministic dynamics Maxwell-demon boundary conditions entropy production space-phase volume contraction 


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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • N. I. Chernov
    • 1
  • J. L. Lebowitz
    • 2
  1. 1.Department of MathematicsUniversity of Alabama in BirminghamBirmingham
  2. 2.Department of MathematicsRutgers UniversityNew Brunswick

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