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Stochastic boundary conditions for interactions with a particle reservoir arediscussed in many-particle systems. We introduce the boundary conditions withthe injection rate and the momentum distribution of particles coming from aparticle reservoir in terms of the pressure and the temperature of thereservoir. It is shown that equilibrium ideal gases and hard-disk systems withthese boundary conditions reproduce statistical-mechanical properties based onthe corresponding grand canonical distributions. We also apply the stochasticboundary conditions to a hard-disk model with a steady particle currentescaping from a particle reservoir in an open tube, and discuss itsnonequilibrium properties such as a chemical potential dependence of thecurrent and deviations from the local equilibrium hypothesis.

Stochastic boundary approaches to many-particle systems coupled to a particle reservoir