{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:33:37Z","timestamp":1760236417078,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T00:00:00Z","timestamp":1637971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11688101"],"award-info":[{"award-number":["11688101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Recently, Savar\u00e9-Toscani proved that the R\u00e9nyi entropy power of general probability densities solving the p-nonlinear heat equation in Rn is a concave function of time under certain conditions of three parameters n,p,\u03bc, which extends Costa\u2019s concavity inequality for Shannon\u2019s entropy power to the R\u00e9nyi entropy power. In this paper, we give a condition \u03a6(n,p,\u03bc) of n,p,\u03bc under which the concavity of the R\u00e9nyi entropy power is valid. The condition \u03a6(n,p,\u03bc) contains Savar\u00e9-Toscani\u2019s condition as a special case and much more cases. Precisely, the points (n,p,\u03bc) satisfying Savar\u00e9-Toscani\u2019s condition consist of a two-dimensional subset of R3, and the points satisfying the condition \u03a6(n,p,\u03bc) consist a three-dimensional subset of R3. Furthermore, \u03a6(n,p,\u03bc) gives the necessary and sufficient condition in a certain sense. Finally, the conditions are obtained with a systematic approach.<\/jats:p>","DOI":"10.3390\/e23121593","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T05:23:02Z","timestamp":1638163382000},"page":"1593","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Generalization of the Concavity of R\u00e9nyi Entropy Power"],"prefix":"10.3390","volume":"23","author":[{"given":"Laigang","family":"Guo","sequence":"first","affiliation":[{"name":"Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3349-533X","authenticated-orcid":false,"given":"Chun-Ming","family":"Yuan","sequence":"additional","affiliation":[{"name":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Shan","family":"Gao","sequence":"additional","affiliation":[{"name":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,27]]},"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 communications","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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