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Entropy
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Entropic and Complexity Measures in Atomic and Molecular Systems
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Entropic and Complexity Measures in Atomic and Molecular Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (26 September 2022) | Viewed by 9574

Special Issue Editors

Prof. Dr. Juan Carlos Angulo

E-Mail Website
Guest Editor
1. Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
2. Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain
Interests: entropic functionals; complexity measures; information planes; atomic and molecular distributions; neutral and ionized systems; quantum similarity and divergence; uncertainty inequalities; relative and mutual information
Dr. Sheila López-Rosa

E-Mail Website
Guest Editor
1. Departamento de Física Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain
2. Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, 41012 Sevilla, Spain
Interests: information theory of quantum systems; entropies, complexities, and divergence measures; atomic and molecular systems; quantum entanglement; mutual information; quantum similarity

Special Issue Information

Dear Colleagues,

The structural features of atomic and molecular systems are known to be strongly related with many of their physical and chemical properties. It is usual to describe their structure in terms of the respective one- and two-particle electron densities, well-defined from the corresponding wavefunctions and straightforwardly interpreted as probability distributions. Within a probabilistic context, information theory plays a central role for an accurate description of the associated uncertainty on the variables involved, and its interpretation in physical terms. Shannon entropy or Fisher information are different examples of entropic descriptors with successful applications on those systems, but many others have also been considered or are emerging at present. Such is the case of complexity measures, frequently but not always derived from the above entropic ones. It is also worth mentioning the variety of relative measures among distributions (e.g., relative information, generalized entropies and divergences) or among variables (e.g., mutual information, conjugated spaces).

The present Special Issue is open to novel contributions on the above topics, but also to others related to them, taking into account the wideness of information theory and its applications. Both analytical and computational results are of interest, as well as the descriptions based on continuous or discrete variables.

Prof. Dr. Juan Carlos Angulo
Dr. Sheila López-Rosa
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • applications of information theory
  • entropy and complexity
  • similarity and divergence
  • atomic and molecular structure
  • electron distributions
  • relative information
  • mutual information
  • ionization and chemical reaction
  • position and momentum spaces

Published Papers (6 papers)

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Editorial

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3 pages, 160 KiB  
Editorial
Entropic and Complexity Measures in Atomic and Molecular Systems
by Juan Carlos Angulo and Sheila López-Rosa
Entropy 2023, 25(2), 367; https://0-doi-org.brum.beds.ac.uk/10.3390/e25020367 - 17 Feb 2023
Viewed by 963
Abstract
Both entropy and complexity are central concepts for the understanding and development of Information Theory, playing an essential role in the increasingly numerous applications in a huge diversity of fields [...] Full article
(This article belongs to the Special Issue Entropic and Complexity Measures in Atomic and Molecular Systems)

Research

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21 pages, 632 KiB  
Article
Shannon Entropy in LS-Coupled Configuration Space for Ni-like Isoelectronic Sequence
by Jian-Jie Wan, Jie Gu, Jiao Li and Na Guo
Entropy 2022, 24(2), 267; https://0-doi-org.brum.beds.ac.uk/10.3390/e24020267 - 12 Feb 2022
Cited by 2 | Viewed by 1959
Abstract
The Shannon entropy in an LS-coupled configuration space has been calculated through a transformation from that in a jj-coupled configuration space for a Ni-like isoelectronic sequence. The sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction have been presented [...] Read more.
The Shannon entropy in an LS-coupled configuration space has been calculated through a transformation from that in a jj-coupled configuration space for a Ni-like isoelectronic sequence. The sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction have been presented for adjacent levels. It is shown that eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, and both of them are a sufficient condition for information exchange, which is the same as the case of the jj-coupled configuration space. It is found that the structure of sudden change from jj-coupled into LS-coupled configuration spaces through the LS-jj transformation is invariant for Shannon entropy along the isoelectronic sequence. What is more, in an LS-coupled configuration space, there are a large number of information exchanges between energy levels whether with or without strong configuration interaction, and most of the ground and single excited states of Ni-like ions are more suitable to be described by a jj-coupled or other configuration basis set instead of an LS-coupled configuration basis set according to the configuration mixing coefficients and their Shannon entropy. In this sense, Shannon entropy can also be used to measure the applicability of a configuration basis set or the purity of atomic state functions in different coupling schemes. Full article
(This article belongs to the Special Issue Entropic and Complexity Measures in Atomic and Molecular Systems)
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23 pages, 485 KiB  
Article
Mutual Information in Conjugate Spaces for Neutral Atoms and Ions
by Juan Carlos Angulo and Sheila López-Rosa
Entropy 2022, 24(2), 233; https://0-doi-org.brum.beds.ac.uk/10.3390/e24020233 - 02 Feb 2022
Cited by 6 | Viewed by 1212
Abstract
The discrepancy among one-electron and two-electron densities for diverse N-electron atomss, enclosing neutral systems (with nuclear charge Z=N) and charge-one ions (|N−Z|=1), is quantified by means of mutual information, I, [...] Read more.
The discrepancy among one-electron and two-electron densities for diverse N-electron atomss, enclosing neutral systems (with nuclear charge Z=N) and charge-one ions (|N−Z|=1), is quantified by means of mutual information, I, and Quantum Similarity Index, QSI, in the conjugate spaces position/momentum. These differences can be interpreted as a measure of the electron correlation of the system. The analysis is carried out by considering systems with a nuclear charge up to Z=103 and singly charged ions (cations and anions) as far as N=54. The interelectronic correlation, for any given system, is quantified through the comparison of its double-variable electron pair density and the product of the respective one-particle densities. An in-depth study along the Periodic Table reveals the importance, far beyond the weight of the systems considered, of their shell structure. Full article
(This article belongs to the Special Issue Entropic and Complexity Measures in Atomic and Molecular Systems)
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12 pages, 8280 KiB  
Article
Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models
by Angel Ricardo Plastino, Diana Monteoliva and Angelo Plastino
Entropy 2021, 23(11), 1488; https://0-doi-org.brum.beds.ac.uk/10.3390/e23111488 - 10 Nov 2021
Cited by 5 | Viewed by 1353
Abstract
Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems [...] Read more.
Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems. In this work we explore the main features of information and information-based complexity indicators in exactly soluble many-fermion models of the Lipkin kind. Models of this kind have been extremely useful in shedding light on the intricacies of quantum many body physics. Models of the Lipkin kind play, for finite systems, a role similar to the one played by the celebrated Hubbard model of solid state physics. We consider two many fermion systems and show how their differences can be best appreciated by recourse to information theoretic tools. We appeal to information measures as tools to compare the structural details of different fermion systems. We will discover that few fermion systems are endowed by a much larger complexity-degree than many fermion ones. The same happens with the coupling-constants strengths. Complexity augments as they decrease, without reaching zero. Also, the behavior of the two lowest lying energy states are crucial in evaluating the system’s complexity. Full article
(This article belongs to the Special Issue Entropic and Complexity Measures in Atomic and Molecular Systems)
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22 pages, 985 KiB  
Article
Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †
by Roman F. Nalewajski
Entropy 2021, 23(4), 483; https://0-doi-org.brum.beds.ac.uk/10.3390/e23040483 - 19 Apr 2021
Cited by 4 | Viewed by 1590
Abstract
In this article, sources of information in electronic states are reexamined and a need for the resultant measures of the entropy/information content, combining contributions due to probability and phase/current densities, is emphasized. Probability distribution reflects the wavefunction modulus and generates classical contributions to [...] Read more.
In this article, sources of information in electronic states are reexamined and a need for the resultant measures of the entropy/information content, combining contributions due to probability and phase/current densities, is emphasized. Probability distribution reflects the wavefunction modulus and generates classical contributions to Shannon’s global entropy and Fisher’s gradient information. The phase component of molecular states similarly determines their nonclassical supplements, due to probability “convection”. The local-energy concept is used to examine the phase equalization in the equilibrium, phase-transformed states. Continuity relations for the wavefunction modulus and phase components are reexamined, the convectional character of the local source of the resultant gradient information is stressed, and latent probability currents in the equilibrium (stationary) quantum states are related to the horizontal (“thermodynamic”) phase. The equivalence of the energy and resultant gradient information (kinetic energy) descriptors of chemical processes is stressed. In the grand-ensemble description, the reactivity criteria are defined by the populational derivatives of the system average electronic energy. Their entropic analogs, given by the associated derivatives of the overall gradient information, are shown to provide an equivalent set of reactivity indices for describing the charge transfer phenomena. Full article
(This article belongs to the Special Issue Entropic and Complexity Measures in Atomic and Molecular Systems)
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Review

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16 pages, 351 KiB  
Review
High Dimensional Atomic States of Hydrogenic Type: Heisenberg-like and Entropic Uncertainty Measures
by Jesús S. Dehesa
Entropy 2021, 23(10), 1339; https://0-doi-org.brum.beds.ac.uk/10.3390/e23101339 - 14 Oct 2021
Cited by 3 | Viewed by 1215
Abstract
High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The D-dimensional hydrogenic system (i.e., a negatively-charged particle moving around a positively charged core under a Coulomb-like potential) [...] Read more.
High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The D-dimensional hydrogenic system (i.e., a negatively-charged particle moving around a positively charged core under a Coulomb-like potential) is the main prototype of the physics of multidimensional quantum systems. In this work, we review the leading terms of the Heisenberg-like (radial expectation values) and entropy-like (Rényi, Shannon) uncertainty measures of this system at the limit of high D. They are given in a simple compact way in terms of the space dimensionality, the Coulomb strength and the state’s hyperquantum numbers. The associated multidimensional position–momentum uncertainty relations are also revised and compared with those of other relevant systems. Full article
(This article belongs to the Special Issue Entropic and Complexity Measures in Atomic and Molecular Systems)
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