The relative entropy is fundamental to multiscale and inverse thermodynamic problems

We show that the relative entropy, S(rel) identical with Sigma(p(T)) ln(p(T)/p(M)), provides a fundamental and unifying framework for multiscale analysis and for inverse molecular-thermodynamic problems involving optimization of a model system (M) to reproduce the properties of a target one (T). We demonstrate that the relative entropy serves as a generating function for principles in variational mean-field theory and uniqueness and gives intuitive results for simple case scenarios in model development. Moreover, we suggest that the relative entropy provides a rigorous framework for multiscale simulations and offers new numerical techniques for linking models at different scales. Finally, we show that S(rel)…