{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:29:11Z","timestamp":1760243351203,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2014,10,15]],"date-time":"2014-10-15T00:00:00Z","timestamp":1413331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Both the Kullback\u2013Leibler and the Tsallis divergence have a strong limitation: if the value zero appears in probability distributions (p1, \u00b7\u00b7\u00b7 , pn) and (q1, \u00b7\u00b7\u00b7 , qn), it must appear in the same positions for the sake of significance. In order to avoid that limitation in the framework of Shannon statistics, Ferreri introduced in 1980 hypoentropy: \u201csuch conditions rarely occur in practice\u201d. The aim of the present paper is to extend Ferreri\u2019s hypoentropy to the Tsallis statistics. We introduce the Tsallis hypoentropy and the Tsallis hypodivergence and describe their mathematical behavior. Fundamental properties, like nonnegativity, monotonicity, the chain rule and subadditivity, are established.<\/jats:p>","DOI":"10.3390\/e16105377","type":"journal-article","created":{"date-parts":[[2014,10,15]],"date-time":"2014-10-15T10:49:43Z","timestamp":1413370183000},"page":"5377-5399","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["On Some Properties of Tsallis Hypoentropies and Hypodivergences"],"prefix":"10.3390","volume":"16","author":[{"given":"Shigeru","family":"Furuichi","sequence":"first","affiliation":[{"name":"Department of Information Science, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Flavia-Corina","family":"Mitroi-Symeonidis","sequence":"additional","affiliation":[{"name":"Faculty of Engineering Sciences, LUMINA - University of South-East Europe, \u00b8 Sos. Colentina 64b, Bucharest, RO-021187, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eleutherius","family":"Symeonidis","sequence":"additional","affiliation":[{"name":"Mathematisch-Geographische Fakult\u00e4t, Katholische Universit\u00e4t Eichst\u00e4tt-Ingolstadt, 85071 Eichst\u00e4tt, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,10,15]]},"reference":[{"key":"ref_1","first-page":"679","article-title":"Einige allgemeine S\u00e4tze \u00fcber W\u00e4rmegleichgewicht","volume":"63","author":"Boltzmann","year":"1871","journal-title":"Wiener Berichte"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gibbs, J.W. (1902). 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