Shannon entropy and many-electron correlations: Theoretical concepts, numerical results, and Collins conjecture

In this article, I will discuss the overlap between the concept of Shannon entropy and the concept of electronic correlation. Quantum Monte Carlo numerical results for the uniform electron gas are also presented; these latter on the one hand enhance the hypothesis of a direct link between the two concepts but on the other hand leave a series of open questions which may be used to trace a roadmap for the future research in the field. © 2014 Wiley Periodicals, Inc. Links between the electron density of DFT and the many‐body wavefunctions/correlations are put forward in terms of encoding/decoding concepts of information theory. In particular, the concept of Shannon entropy can be employed into the development of electronic correlation functionals, and the Hohenberg−Kohn theorem be seen as a specific case of a more general encoding process.