Phase diagram and density large deviations of a nonconserving ABC model
  The effect of particle-nonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized ABC model. It is shown that in the limit of slow nonconserving processes, the large deviation function of the overall particle density can be computed by making use of the steady state density profile of the conserving model. In this limit one can define a chemical potential and identify first order transitions via Maxwell's construction, similarly to what is done in equilibrium systems. This method may be applied to other driven models subjected to slow nonconserving dynamics. 
Or Cohen, David Mukamel
cond-mat.stat-mech