Predicting the thermodynamics by using state-dependent interactions

We reconsider the structure-based route to coarse graining in which the coarse-grained model is defined in such a way to reproduce some distributions functions of the original system as accurately as possible. We elucidate why standard expressions for pressure and chemical potential applied to this family of coarse-grained models with density-dependent interactions fail to reproduce pressure and chemical potential of the underlying original system, under the only assumption that the interactions in the underlying model be state independent. Moreover, we show that the state- dependent potentials depend on the ensemble in which they have been derived. Therefore, care must be used in applying canonical state-dependent potentials to predict phase lines, which is typically performed in other ensembles.