{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T05:10:47Z","timestamp":1776748247805,"version":"3.51.2"},"reference-count":56,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T00:00:00Z","timestamp":1622505600000},"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 measures of information transfer which correspond to non-additive entropies have intensively been studied in previous decades. The majority of the work includes the ones belonging to the Sharma\u2013Mittal entropy class, such as the R\u00e9nyi, the Tsallis, the Landsberg\u2013Vedral and the Gaussian entropies. All of the considerations follow the same approach, mimicking some of the various and mutually equivalent definitions of Shannon information measures, and the information transfer is quantified by an appropriately defined measure of mutual information, while the maximal information transfer is considered as a generalized channel capacity. However, all of the previous approaches fail to satisfy at least one of the ineluctable properties which a measure of (maximal) information transfer should satisfy, leading to counterintuitive conclusions and predicting nonphysical behavior even in the case of very simple communication channels. This paper fills the gap by proposing two parameter measures named the \u03b1-q-mutual information and the \u03b1-q-capacity. In addition to standard Shannon approaches, special cases of these measures include the \u03b1-mutual information and the \u03b1-capacity, which are well established in the information theory literature as measures of additive R\u00e9nyi information transfer, while the cases of the Tsallis, the Landsberg\u2013Vedral and the Gaussian entropies can also be accessed by special choices of the parameters \u03b1 and q. It is shown that, unlike the previous definition, the \u03b1-q-mutual information and the \u03b1-q-capacity satisfy the set of properties, which are stated as axioms, by which they reduce to zero in the case of totally destructive channels and to the (maximal) input Sharma\u2013Mittal entropy in the case of perfect transmission, which is consistent with the maximum likelihood detection error. In addition, they are non-negative and less than or equal to the input and the output Sharma\u2013Mittal entropies, in general. Thus, unlike the previous approaches, the proposed (maximal) information transfer measures do not manifest nonphysical behaviors such as sub-capacitance or super-capacitance, which could qualify them as appropriate measures of the Sharma\u2013Mittal information transfer.<\/jats:p>","DOI":"10.3390\/e23060702","type":"journal-article","created":{"date-parts":[[2021,6,1]],"date-time":"2021-06-01T23:07:03Z","timestamp":1622588823000},"page":"702","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On the \u03b1-q-Mutual Information and the \u03b1-q-Capacities"],"prefix":"10.3390","volume":"23","author":[{"given":"Velimir M.","family":"Ili\u0107","sequence":"first","affiliation":[{"name":"Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Beograd, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0764-0268","authenticated-orcid":false,"given":"Ivan B.","family":"Djordjevi\u0107","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Arizona, 1230 E. 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