{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T09:18:09Z","timestamp":1762075089512,"version":"build-2065373602"},"reference-count":111,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T00:00:00Z","timestamp":1667347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Junta de Andaluc\u00eda","award":["P20-00082","PID2020-113390GB-I00","FQM-207"],"award-info":[{"award-number":["P20-00082","PID2020-113390GB-I00","FQM-207"]}]},{"name":"Agencia Estatal de Investigaci\u00f3n (Spain)","award":["P20-00082","PID2020-113390GB-I00","FQM-207"],"award-info":[{"award-number":["P20-00082","PID2020-113390GB-I00","FQM-207"]}]},{"name":"European Regional Development Fund","award":["P20-00082","PID2020-113390GB-I00","FQM-207"],"award-info":[{"award-number":["P20-00082","PID2020-113390GB-I00","FQM-207"]}]},{"name":"Agencia de Innovaci\u00f3n y Desarrollo de Andaluc\u00eda","award":["P20-00082","PID2020-113390GB-I00","FQM-207"],"award-info":[{"award-number":["P20-00082","PID2020-113390GB-I00","FQM-207"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The various facets of the internal disorder of quantum systems can be described by means of the R\u00e9nyi entropies of their single-particle probability density according to modern density functional theory and quantum information techniques. In this work, we first show the lower and upper bounds for the R\u00e9nyi entropies of general and central-potential quantum systems, as well as the associated entropic uncertainty relations. Then, the R\u00e9nyi entropies of multidimensional oscillator and hydrogenic-like systems are reviewed and explicitly determined for all bound stationary position and momentum states from first principles (i.e., in terms of the potential strength, the space dimensionality and the states\u2019s hyperquantum numbers). This is possible because the associated wavefunctions can be expressed by means of hypergeometric orthogonal polynomials. Emphasis is placed on the most extreme, non-trivial cases corresponding to the highly excited Rydberg states, where the R\u00e9nyi entropies can be amazingly obtained in a simple, compact, and transparent form. Powerful asymptotic approaches of approximation theory have been used when the polynomial\u2019s degree or the weight-function parameter(s) of the Hermite, Laguerre, and Gegenbauer polynomials have large values. At present, these special states are being shown of increasing potential interest in quantum information and the associated quantum technologies, such as e.g., quantum key distribution, quantum computation, and quantum metrology.<\/jats:p>","DOI":"10.3390\/e24111590","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T03:11:21Z","timestamp":1667445081000},"page":"1590","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["R\u00e9nyi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4397-9426","authenticated-orcid":false,"given":"Jes\u00fas","family":"Dehesa","sequence":"first","affiliation":[{"name":"Instituto Carlos I de F\u00edsica Te\u00f3rica y Computacional, Universidad de Granada, 18071 Granada, Spain"},{"name":"Departamento de F\u00edsica At\u00f3mica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,2]]},"reference":[{"key":"ref_1","first-page":"547","article-title":"On measures of information and entropy","volume":"Volume 1","author":"Neyman","year":"1961","journal-title":"Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_2","unstructured":"R\u00e9nyi, A. 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