Euler-scale hydrodynamics without attractiveness

Prove hydrodynamic limits at Euler scaling for asymmetric interacting particle systems with drift that neither satisfy the basic coupling nor possess the attractiveness property.

Background

The relative entropy argument is presented for TASEP, an attractive asymmetric exclusion process, and relies on a one-block estimate. The notes state that hydrodynamics for all times can be obtained for attractive processes by other methods.

For general drifted processes lacking attractiveness, the corresponding all-time Euler-scale hydrodynamic limit remains unresolved. Establishing such a result would extend the theory beyond the class where the basic coupling provides the required comparison and local-equilibrium estimates.