  Stochastic boundary conditions for interactions with a particle reservoir are
discussed in many-particle systems. We introduce the boundary conditions with
the injection rate and the momentum distribution of particles coming from a
particle reservoir in terms of the pressure and the temperature of the
reservoir. It is shown that equilibrium ideal gases and hard-disk systems with
these boundary conditions reproduce statistical-mechanical properties based on
the corresponding grand canonical distributions. We also apply the stochastic
boundary conditions to a hard-disk model with a steady particle current
escaping from a particle reservoir in an open tube, and discuss its
nonequilibrium properties such as a chemical potential dependence of the
current and deviations from the local equilibrium hypothesis.
