Hydrodynamic limits of collisions and fluxes in the exclusion process

TL;DR

This paper extends the hydrodynamic description of the symmetric exclusion process by incorporating collision events, revealing regime-dependent limits and clarifying microscopic blocking effects at macroscopic and fluctuation levels.

Contribution

It introduces a detailed analysis of collision and flux observables in the exclusion process, providing a quantitative decomposition into transport and collision effects.

Findings

Collision counts have stochastic white noise limits.

Unidirectional fluxes exhibit deterministic hydrodynamic limits.

Microscopic blocking effects manifest at macroscopic and fluctuation levels.

Abstract

We extend the usual hydrodynamic description of the symmetric exclusion process by keeping track of collision events corresponding to jumps into already occupied sites, thereby quantifying the dissipated part of the microscopic activity that is otherwise discarded by the empirical density in the macroscopic limit. In addition to the empirical density and net current, we study unidirectional fluxes and collision counts under flexible joint scalings of the lattice spacing and particle number. These collision and flux observables have regime dependent hydrodynamic limits, with deterministic unidirectional behaviour and a stochastic space time white noise limit for the net collision count. Our results provide a quantitative decomposition of exclusion dynamics into transport and collision effects and clarify how microscopic blocking manifests at the macroscopic and fluctuation levels.