Statistical Mechanics of Density- and Temperature-Dependent Potentials: Application to Condensed Phases within GenDPDE

for supercritical Ar). Remarkably, we show that the model is also valid in a range of thermodynamic conditions near the reference states, allowing for a correct description of the physics of systems with spatial density and temperature variations. We furthermore derive analytical expressions for the macroscopic pressure and energy equations of state in terms of the model parameters, discussing their validity and limitations. We show that, even at the mean-field level, a correct account of the local particle arrangements is necessary to obtain accurate predictions of the macroscopic thermodynamic quantities from mesoscopic properties. Thus, we also investigate the applicability of the Hypernetted Chain approximation as a tool to predict the radial distribution function of the GenDPDE system, examining the strengths and deficiencies of this approach. With the proposed LTh model, GenDPDE provides a reliable and flexible tool for the analysis of condensed phases through coarse-grain techniques.