Hydrodynamic limit of mean zero asymmetric zero range processes in infinite volume

We prove the hydrodynamic behaviour of mean zero, asymmetric zero range processes evolving on the infinite lattice Z(d). The proof relies on a bound, uniform in the volume, for the entropy production of processes in large finite volume. Such an entropy production bound, uniform in the volume, was first proved by Fritz in [6] to extend to infinite volume the proof of Guo Papanicolaou and Varadhan of hydrodynamic behaviour of interacting particle systems, Our approach follows a method introduced by Yau in [12].