The relative entropy is fundamental to multiscale and inverse thermodynamic problems

We show that the relative entropy, S rel ≡ ∑ 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...

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Bibliographic Details
Published in:The Journal of chemical physics 2008-10, Vol.129 (14), p.144108-144108-7
Main Author: Shell, M. Scott
Format: Article
Language:English
Subjects:
Algorithms
Diffusion
Entropy
Kinetics
Likelihood Functions
Models, Chemical
Water - chemistry
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Summary:We show that the relative entropy, S rel ≡ ∑ 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 carries physical significance by using it to quantify the deviations of a three-site model of water from simple liquids, finding that the relative entropy, a thermodynamic concept, even predicts water's kinetic anomalies.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.2992060