In this study we explore a systematic procedure to coarsen a microscopic model towards a mesoscopic model. The procedure is applied to a system of chains of ten beads, representing a low molecular weight polymer melt. Our method consists of defining coarse-grained sites in the microscopic system, and calculating their spatial distribution on the pair level.The effective interaction betweent he coarse-grained sites is then obtianed by bringing the pair interactionin consistence with the pair density. We investigate both a dynamic and a stochastic method for this step. The so obtianed mesoscopic interactionis used in a molecular dynamics simulation to investigate the pressure of the coarse-grained system. We found that the pair interaction that reproduces the pair dnesity predicts pressure that is significantly lower than the microscopic value, even if we take the state-dependency of the coarse-grained interactions into account. We therefore conclude that coarse-grained models lack thermodynamic consistency.
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