{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T17:00:41Z","timestamp":1763830841840,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,11,12]],"date-time":"2017-11-12T00:00:00Z","timestamp":1510444800000},"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>The aim of this paper is to show that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can be determined uniquely only when one fixes the prescription for handling conditional entropies. By using the concept of Kolmogorov\u2013Nagumo quasi-linear means, we prove this with the help of Dar\u00f3tzy\u2019s mapping theorem. Our point is further illustrated with a number of explicit examples. Other salient issues, such as connections of conditional entropies with the de Finetti\u2013Kolmogorov theorem for escort distributions and with Landsberg\u2019s classification of non-extensive thermodynamic systems are also briefly discussed.<\/jats:p>","DOI":"10.3390\/e19110605","type":"journal-article","created":{"date-parts":[[2017,11,13]],"date-time":"2017-11-13T11:12:36Z","timestamp":1510571556000},"page":"605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On the Uniqueness Theorem for Pseudo-Additive Entropies"],"prefix":"10.3390","volume":"19","author":[{"given":"Petr","family":"Jizba","sequence":"first","affiliation":[{"name":"Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, Prague 115 19, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5371-5320","authenticated-orcid":false,"given":"Jan","family":"Korbel","sequence":"additional","affiliation":[{"name":"Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, Prague 115 19, Czech Republic"},{"name":"Section for Science of Complex Systems, CeMSIIS, Medical University of Vienna, Spitalgasse 23, Vienna 1090, Austria"},{"name":"Complexity Science Hub Vienna, Josefst\u00e4dterstrasse 39, Vienna 1090, Austria"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,12]]},"reference":[{"key":"ref_1","unstructured":"Tsallis, C. 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