Coarse-Graining Entropy, Forces, and Structures

The maximum likelihood-based Relative Entropy and force-matching-based Multiscale Coarse-graining methods are two distinct variational approaches for parameterizing a coarse-grained model based on a higher resolution model. This work presents a rigorous comparison of these methods and, most significantly, shows that they can both be viewed in terms of the same information function. The resulting insight clarifies limitations of both approaches and suggests a more general variational principle.