  We consider a family of models having an arbitrary positive amount of mass on
each site and randomly exchanging an arbitrary amount of mass with nearest
neighbor sites. We restrict to the case of diffusive models. We identify a
class of reversible models for which the product invariant measure is known and
the gradient condition is satisfied so that we can explicitly compute the
transport coefficients associated to the diffusive hydrodynamic rescaling.
Based on the Macroscopic Fluctuation Theory \cite{mft} we have that the large
deviations rate functional for a stationary non equilibrium state can be
computed solving a Hamilton-Jacobi equation depending only on the transport
coefficients and the details of the boundary sources. Thus, we are able to
identify a class of models having transport coefficients for which the
Hamilton-Jacobi equation can indeed be solved. We give a complete
characterization in the case of generalized zero range models and discuss
several other cases. For the generalized zero range models we identify a class
of discrete models that, modulo trivial extensions, coincides with the class
discussed in \cite{FG} and a class of continuous dynamics that coincides with
the class in \cite{FFG}. Along the discussion we obtain a complete
characterization of reversible misanthrope processes solving the discrete
equations in \cite{CC}.
