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