Shannon Entropy and Many-Electron Correlations: Theoretical Concepts, Numerical Results and Collins Conjecture

TL;DR

This paper explores the relationship between Shannon Entropy and electronic correlation, presenting quantum Monte Carlo results for the uniform electron gas to support the hypothesis of a direct link and outlining future research directions.

Contribution

It introduces a theoretical connection between Shannon Entropy and many-electron correlations, supported by numerical results and open questions for future studies.

Findings

Quantum Monte Carlo results support the link between entropy and correlation.

Open questions identified for future research.

Enhanced understanding of entropy's role in electronic systems.

Abstract

In this paper 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 employed to trace a roadmap for the future research in the field.