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Factorized steady states for multi-species mass transfer models

A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and sufficient conditions on the mass transfer dynamics under which the steady state factorizes. We generalize the model to mass transfer on arbitrary lattices and present sufficient conditions for factorization. In both cases, explicit results for random sequential update and continuous time limits are given.