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

TL;DR

This paper introduces stochastic boundary conditions for many-particle systems interacting with a particle reservoir, enabling the study of equilibrium and nonequilibrium properties in open systems.

Contribution

It develops boundary conditions based on pressure and temperature that reproduce grand canonical distributions and applies them to nonequilibrium steady states.

Findings

Reproduces grand canonical distributions in equilibrium systems.

Demonstrates nonequilibrium steady states with particle currents.

Shows deviations from local equilibrium in open systems.

Abstract

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.