Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup>
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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/4/483 |
| _version_ | 1797537147267317760 |
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| author | Roman F. Nalewajski |
| author_facet | Roman F. Nalewajski |
| author_sort | Roman F. Nalewajski |
| collection | DOAJ |
| 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 <i>classical</i> contributions to Shannon’s global entropy and Fisher’s gradient information. The phase component of molecular states similarly determines their <i>nonclassical</i> supplements, due to probability “convection”. The local-energy concept is used to examine the <i>phase</i> equalization in the equilibrium, <i>phase</i>-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 <i>horizontal</i> (“thermodynamic”) phase. The equivalence of the energy and resultant gradient information (kinetic energy) descriptors of chemical processes is stressed. In the <i>grand</i>-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. |
| first_indexed | 2024-03-10T12:11:53Z |
| format | Article |
| id | doaj.art-cabdb160e67c47cc81ae661d64324d25 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T12:11:53Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-cabdb160e67c47cc81ae661d64324d252023-11-21T16:11:59ZengMDPI AGEntropy1099-43002021-04-0123448310.3390/e23040483Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup>Roman F. Nalewajski0Department of Theoretical Chemistry, Jagiellonian University, Gronostajowa 2, 30-387 Cracow, PolandIn 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 <i>classical</i> contributions to Shannon’s global entropy and Fisher’s gradient information. The phase component of molecular states similarly determines their <i>nonclassical</i> supplements, due to probability “convection”. The local-energy concept is used to examine the <i>phase</i> equalization in the equilibrium, <i>phase</i>-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 <i>horizontal</i> (“thermodynamic”) phase. The equivalence of the energy and resultant gradient information (kinetic energy) descriptors of chemical processes is stressed. In the <i>grand</i>-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.https://www.mdpi.com/1099-4300/23/4/483continuity relationsgrand ensembleinformation sourcesphase equalizationreactivity criteriaresultant information |
| spellingShingle | Roman F. Nalewajski Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup> Entropy continuity relations grand ensemble information sources phase equalization reactivity criteria resultant information |
| title | Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup> |
| title_full | Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup> |
| title_fullStr | Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup> |
| title_full_unstemmed | Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup> |
| title_short | Resultant Information Descriptors, Equilibrium States and Ensemble Entropy <sup>†</sup> |
| title_sort | resultant information descriptors equilibrium states and ensemble entropy sup † sup |
| topic | continuity relations grand ensemble information sources phase equalization reactivity criteria resultant information |
| url | https://www.mdpi.com/1099-4300/23/4/483 |
| work_keys_str_mv | AT romanfnalewajski resultantinformationdescriptorsequilibriumstatesandensembleentropysupsup |