{"paper":{"title":"$r$-deformed $\\alpha$-$z$-R\\'enyi relative entropy","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.IT","math.FA","math.IT","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Shigeru Furuichi, Srikrishna Maity, Supriyo Dutta","submitted_at":"2026-07-02T07:19:09Z","abstract_excerpt":"In this article, we consider the $r$-logarithm for defining three-parameter family of R\\'{e}nyi relative entropies that are generalization of the $\\alpha$-$z$-R\\'{e}nyi relative entropies. All the members of $r$-deformed $\\alpha$-$z$-R\\'{e}nyi relative entropies satisfy the necessary axioms to be a divergence. We expose the range of parameters $\\alpha$, $z$ and $r$ for which the data processing inequality holds. We also establish that $r$-deformed $\\alpha$-$z$-R\\'{e}nyi relative entropy is an upper bound of the Tsallis relative entropy. Now, we have two upper bounds of the Tsallis relative ent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01805","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01805/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}