We show that the relative entropy, $S_{\text{rel}}$, suggests a fundamental indicator of the success of multiscale studies, in which coarse-grained (CG) models are linked to first-principles (FP) ones. We demonstrate that $S_{\text{rel}}$ inherently measures fluctuations in the differences between CG and FP potential energy landscapes, and develop a theory that tightly and generally links it to errors associated with coarse graining. We consider two simple case studies substantiating these results, and suggest that $S_{\text{rel}}$ has important ramifications for evaluating and designing coarse-grained models.

• Received 28 April 2010

DOI:https://doi.org/10.1103/PhysRevE.81.060104