Statistical Complexity and Fisher-Shannon Information. Applications

TL;DR

This paper introduces and discusses statistical measures of complexity and Fisher-Shannon information, demonstrating their application to various quantum systems to reveal conformational properties.

Contribution

It presents new statistical indicators based on Shannon information and Fisher information, applied to diverse quantum systems for the first time.

Findings

Indicators distinguish different quantum conformations

Measures highlight properties of atomic and molecular systems

Applications include atoms, ions, and the periodic table

Abstract

In this chapter, a statistical measure of complexity and the Fisher-Shannon information product are introduced and their properties are discussed. These measures are based on the interplay between the Shannon information, or a function of it, and the separation of the set of accessible states to a system from the equiprobability distribution, i.e. the disequilibrium or the Fisher information, respectively. Different applications in discrete and continuous systems are shown. Some of them are concerned with quantum systems, from prototypical systems such as the H-atom, the harmonic oscillator and the square well to other ones such as He-like ions, Hooke's atoms or just the periodic table. In all of them, these statistical indicators show an interesting behavior able to discern and highlight some conformational properties of those systems.