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We study a mass transport model on a ring with parallel update, where acontinuous mass is randomly redistributed along distinct links of the lattice,choosing at random one of the two partitions at each time step. Theredistribution process on a given link depends on the masses on both sites, atvariance with the Zero Range Process and its continuous mass generalizations.We show that the steady-state distribution takes a simple non-factorized formthat can be written as a sum of two inhomogeneous product measures. Afactorized measure is recovered for a symmetric mass redistribution,corresponding to an equilibrium process. A non-equilibrium free energy can beexplicitly defined from the partition function. We evaluate differentcharacterizations of the `distance' to equilibrium, either dynamic or static:the mass flux, the entropy production rate, the Gibbs free-energy differencebetween the equilibrium and non-equilibrium stationary states, and thederivative of the non-equilibrium free energy with respect to the applieddriving force. The connection between these different non-equilibriumparameters is discussed.

A mass transport model with a simple non-factorized steady-state distribution