Predicting the thermodynamics by using state-dependent interactions

TL;DR

This paper examines the limitations of using state-dependent, density-dependent interactions in coarse-grained models to predict thermodynamic properties, highlighting ensemble dependence and approximation issues.

Contribution

It demonstrates that pressure and chemical potential calculations in such models are approximate and depend on the ensemble, providing insights into their applicability and limitations.

Findings

Pressure and chemical potential are approximations in coarse-grained models.

State-dependent potentials vary with the ensemble used.

Care is needed when applying these models to phase diagram predictions.

Abstract

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 consider standard expressions for pressure and chemical potential applied to this family of coarse-grained models with density-dependent interactions and show that they only provide approximations to the pressure and chemical potential of the underlying original system. These approximations are then carefully compared in two cases: we consider a generic microscopic system in the low-density regime and polymer solutions under good-solvent conditions. 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.