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Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †

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...

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Autor principal: Nalewajski, Roman F.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8073102/
https://www.ncbi.nlm.nih.gov/pubmed/33921766
http://dx.doi.org/10.3390/e23040483
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author Nalewajski, Roman F.
author_facet Nalewajski, Roman F.
author_sort Nalewajski, Roman F.
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description 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.
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spelling pubmed-80731022021-04-27 Resultant Information Descriptors, Equilibrium States and Ensemble Entropy † Nalewajski, Roman F. Entropy (Basel) Article 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. MDPI 2021-04-19 /pmc/articles/PMC8073102/ /pubmed/33921766 http://dx.doi.org/10.3390/e23040483 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Nalewajski, Roman F.
Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †
title Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †
title_full Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †
title_fullStr Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †
title_full_unstemmed Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †
title_short Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †
title_sort resultant information descriptors, equilibrium states and ensemble entropy †
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8073102/
https://www.ncbi.nlm.nih.gov/pubmed/33921766
http://dx.doi.org/10.3390/e23040483
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