Coarse Graining of Nonbonded Degrees of Freedom

We investigate the physical meaning of coarse-grained beads generated by coarse graining of nonbonded particles such as solvent molecules in a solution. Starting from the partition function, we analytically coarse grain an $N$-particle fluid to a system containing $N-2$ of the original particles plus a bead representing the two remaining particles. As a direct consequence of the lack of bonding interactions, the resulting effective potential becomes independent of the bead coordinates, i.e., ideal-gas-like, in the thermodynamic limit. Thus, there are no conservative forces between coarse-grained beads representing assemblies of nonbonded molecules nor between these beads and any other species in the system.