  We consider the zero-range process with arbitrary bounded monotone rates on
the complete graph, in the regime where the number of sites diverges while the
density of particles per site converges. We determine the asymptotics of the
mixing time from any initial configuration, and establish the cutoff
phenomenon. The intuitive picture is that the system separates into a slowly
evolving solid phase and a quickly relaxing liquid phase: as time passes, the
solid phase dissolves into the liquid phase, and the mixing time is essentially
the time at which the system becomes completely liquid. Our proof uses the path
coupling technique of Bubley and Dyer, and the analysis of a suitable
hydrodynamic limit. To the best of our knowledge, even the order of magnitude
of the mixing time was unknown, except in the special case of constant rates.
