A generalized mean field theory of coarse-graining.

A general mean field theory is presented for the construction of equilibrium coarse-grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of this theory. The theory also applies to the opposite problem of reduction, where relevant information is extracted from available equilibrium ensemble data. Additionally, a complementary approach is presented and problems of representability in coarse-grained modeling analyzed using information theoretic arguments. These problems are central to the construction of coarse-grained representations of complex systems, and commonly used coarse-graining methods and variational principles for coarse-graining are derived as particular cases of the general theory.