A simple method for the evaluation of the information content and complexity in atoms. A proposal for scalability

TL;DR

This paper introduces a simple, scalable method for evaluating information content and complexity in atoms using fractional occupation probabilities, aligning well with experimental data and offering insights into atomic order and complexity.

Contribution

It proposes a straightforward approach to compute entropy and complexity measures in atoms based on fractional occupation probabilities, simplifying previous methods and enabling scalability.

Findings

Atoms are close to extensive systems with q=1.031.

Complexity does not increase significantly with atomic number Z.

Atoms are ordered systems with limited growth in complexity.

Abstract

We present a very simple method for the calculation of Shannon, Fisher, Onicescu and Tsallis entropies in atoms, as well as SDL and LMC complexity measures, as functions of the atomic number Z. Fractional occupation probabilities of electrons in atomic orbitals are employed, instead of the more complicated continuous electron probability densities in position and momentum spaces, used so far in the literature. Our main conclusions are compatible with the results of more sophisticated approaches and correlate fairly with experimental data. We obtain for the Tsallis entropic index the value q=1.031, which shows that atoms are very close to extensivity. A practical way towards scalability of the quantification of complexity for systems with more components than the atom is indicated. We also discuss the issue if the complexity of the electronic structure of atoms increases with Z. A Pair of Order-Disorder Indices (PODI), which can be introduced for any quantum many-body system, is evaluated in atoms. We conclude that "atoms are ordered systems, which do not grow in complexity as Z increases".