{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T19:03:35Z","timestamp":1774897415643,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,6,14]],"date-time":"2017-06-14T00:00:00Z","timestamp":1497398400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Tsallis entropy given for a positive parameter    \u03b1    can be considered as a generalization of the classical Shannon entropy. For the latter, corresponding to     \u03b1 = 1    , there exist many axiomatic characterizations. One of them based on the well-known Khinchin-Shannon axioms has been simplified several times and adapted to Tsallis entropy, where the axiom of (generalized) Shannon additivity is playing a central role. The main aim of this paper is to discuss this axiom in the context of Tsallis entropy. We show that it is sufficient for characterizing Tsallis entropy, with the exceptions of cases     \u03b1 = 1 , 2     discussed separately.<\/jats:p>","DOI":"10.3390\/axioms6020014","type":"journal-article","created":{"date-parts":[[2017,6,14]],"date-time":"2017-06-14T10:49:53Z","timestamp":1497437393000},"page":"14","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Tsallis Entropy and Generalized Shannon Additivity"],"prefix":"10.3390","volume":"6","author":[{"given":"Sonja","family":"J\u00e4ckle","sequence":"first","affiliation":[{"name":"Institute of Mathematics, University of L\u00fcbeck, D-23562 L\u00fcbeck, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karsten","family":"Keller","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of L\u00fcbeck, D-23562 L\u00fcbeck, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1088\/2058-7058\/27\/05\/39","article-title":"Roll over, Boltzmann","volume":"27","author":"Cartwright","year":"2014","journal-title":"Phys. World"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Tsallis, C. (2016). Approach of complexity in nature: Entropic nonuniqueness. Axioms, 5.","DOI":"10.3390\/axioms5030020"},{"key":"ref_4","first-page":"30","article-title":"Quantification method of classification processes. Concept of structural \u03b1-entropy","volume":"3","author":"Havrda","year":"1967","journal-title":"Kybernetika"},{"key":"ref_5","first-page":"3301","article-title":"On entropy, entropy-like quantities, and applications","volume":"20","author":"Keller","year":"2015","journal-title":"Discrete Contin. Dyn. Syst. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/e18030084","article-title":"Entropy and Fractal Antennas","volume":"18","author":"Guariglia","year":"2016","journal-title":"Entropy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1783","DOI":"10.1109\/TIT.2004.831749","article-title":"Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy","volume":"50","author":"Suyari","year":"2004","journal-title":"IEEE T. Inform. Theory"},{"key":"ref_8","unstructured":"Khinchin, A.I. (1957). Mathematical Foundations of Information Theory, Dover."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"397","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_10","doi-asserted-by":"crossref","first-page":"4104","DOI":"10.1063\/1.532107","article-title":"Generalization of Shannon\u2019s theorem for Tsallis entropy","volume":"38","year":"1997","journal-title":"J. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s00161-003-0153-1","article-title":"Tsallis entropy: How unique?","volume":"16","author":"Abe","year":"2004","journal-title":"Contin. Mech. Thermodyn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3638","DOI":"10.1109\/TIT.2005.855606","article-title":"On uniqueness Theorems for Tsallis entropy and Tsallis relative entropy","volume":"51","author":"Furuichi","year":"2005","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"261","DOI":"10.3390\/e10030261","article-title":"Axiomatic characterizations of information measures","volume":"10","year":"2008","journal-title":"Entropy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6950","DOI":"10.1109\/TIT.2013.2259958","article-title":"Comments on \u201cGeneralization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy\u201d","volume":"59","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/S0019-9958(75)90514-8","article-title":"The role of boundedness in characterizing Shannon entropy","volume":"29","author":"Diderrich","year":"1975","journal-title":"Inf. Control"},{"key":"ref_16","first-page":"227","article-title":"On the concept of entropy of a finite probability scheme","volume":"11","author":"Faddeev","year":"1956","journal-title":"Uspehi Mat. Nauk"},{"key":"ref_17","first-page":"67","article-title":"Nonnegative information functions. Analytic function methods in probability theory","volume":"21","author":"Maksa","year":"1982","journal-title":"Colloq. Math. Soc. Janos Bolyai"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0893-9659(92)90084-M","article-title":"An axiomatic definition of Shannon\u2019s entropy","volume":"5","author":"Nambiar","year":"1992","journal-title":"App. Math. Lett."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/6\/2\/14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:39:06Z","timestamp":1760207946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/6\/2\/14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,14]]},"references-count":18,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,6]]}},"alternative-id":["axioms6020014"],"URL":"https:\/\/doi.org\/10.3390\/axioms6020014","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,14]]}}}