Local equilibrium in planar non interacting particle systems

TL;DR

This paper establishes abstract conditions under which local equilibrium occurs in large planar non-interacting particle systems, verified through examples like iid random walks and the periodic Lorentz process.

Contribution

It introduces a set of abstract conditions ensuring local equilibrium in diffusive scaling limits for non-interacting particle systems, validated in specific models.

Findings

Conditions imply local equilibrium in diffusive scaling.

Conditions verified for iid random walks.

Conditions verified for periodic Lorentz process.

Abstract

Particles are injected to a large planar rectangle through the boundary. Assuming that the particles move independently from one another and the boundary is also absorbing, we identify a set of abstract conditions which imply the local equilibrium of the particle density in diffusive scaling limit. We verify that our abstract conditions hold in two examples: iid random walks and the periodic Lorentz process.