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The thermodynamic entropy of coarse-grained (CG) models stands as one of themost important properties for quantifying the missing information during the CGprocess and for establishing transferable (or extendible) CG interactions.However, performing additional CG simulations on top of model constructionoften leads to significant additional computational overhead. In this work, wepropose a simple hierarchical framework for predicting the thermodynamicentropies of various molecular CG systems. Our approach employs a decompositionof the CG interactions, enabling the estimation of the CG partition functionand thermodynamic properties a priori. Starting from the ideal gas description,we leverage classical perturbation theory to systematically incorporate simpleyet essential interactions, ranging from the hard sphere model to thegeneralized van der Waals model. Additionally, we propose an alternativeapproach based on multiparticle correlation functions, allowing for systematicimprovements through higher-order correlations. Numerical applications tomolecular liquids validate the high fidelity of our approach, and ourcomputational protocols demonstrate that a reduced model with simple energeticscan reasonably estimate the thermodynamic entropy of CG models withoutperforming any CG simulations. Overall, our findings present a systematicframework for estimating not only the entropy but also other thermodynamicproperties of CG models, relying solely on information from the referencesystem.

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models