{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:10:21Z","timestamp":1777367421176,"version":"3.51.4"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T00:00:00Z","timestamp":1587686400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1181558"],"award-info":[{"award-number":["1181558"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>There are entropic functionals galore, but not simple objective measures to distinguish between them. We remedy this situation here by appeal to Born\u2019s proposal, of almost a hundred years ago, that the square modulus of any wave function      | \u03c8 |  2     be regarded as a probability distribution P. the usefulness of using information measures like Shannon\u2019s in this pure-state context has been highlighted in [Phys. Lett. A1993, 181, 446]. Here we will apply the notion with the purpose of generating a dual functional [     F  \u03b1 R   :  {  S Q  }  \u27f6  R +     ], which maps entropic functionals onto positive real numbers. In such an endeavor, we use as standard ingredients the coherent states of the harmonic oscillator (CHO), which are unique in the sense of possessing minimum uncertainty. This use is greatly facilitated by the fact that the CHO can be given analytic, compact closed form as shown in [Rev. Mex. Fis. E 2019, 65, 191]. Rewarding insights are to be obtained regarding the comparison between several standard entropic measures.<\/jats:p>","DOI":"10.3390\/e22040491","type":"journal-article","created":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T11:42:14Z","timestamp":1587728534000},"page":"491","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Useful Dual Functional of Entropic Information Measures"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5934-2783","authenticated-orcid":false,"given":"Angelo","family":"Plastino","sequence":"first","affiliation":[{"name":"Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina"},{"name":"Departamento de F\u00edsica, Universidad Nacional de La Plata, 1900 La Plata, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario Carlos","family":"Rocca","sequence":"additional","affiliation":[{"name":"Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina"},{"name":"Departamento de F\u00edsica, Universidad Nacional de La Plata, 1900 La Plata, Argentina"},{"name":"Departamento de Matem\u00e1tica, Universidad Nacional de La Plata, 1900 La Plata, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Flavia","family":"Pennini","sequence":"additional","affiliation":[{"name":"Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina"},{"name":"Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, 6300 La Pampa, Argentina"},{"name":"Departamento de F\u00edsica, Universidad Cat\u00f3lica del Norte, Av. Angamos 0610, 2340000 Antofagasta, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information Theory and Statistical Mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1103\/PhysRev.108.171","article-title":"Information Theory and Statistical Mechanics. 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