{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:16:15Z","timestamp":1760217375980,"version":"build-2065373602"},"reference-count":103,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,16]],"date-time":"2015-03-16T00:00:00Z","timestamp":1426464000000},"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>Searching for the dynamical foundations of Havrda-Charv\u00e1t\/Dar\u00f3czy\/ Cressie-Read\/Tsallis non-additive entropy, we come across a covariant quantity called, alternatively, a generalized Ricci curvature, an N-Ricci curvature or a Bakry-\u00c9mery-Ricci curvature in the configuration\/phase space of a system. We explore some of the implications of this tensor and its associated curvature and present a connection with the non-additive entropy under investigation. We present an isoperimetric interpretation of the non-extensive parameter and comment on further features of the system that can be probed through this tensor.<\/jats:p>","DOI":"10.3390\/e17031278","type":"journal-article","created":{"date-parts":[[2015,3,16]],"date-time":"2015-03-16T11:17:39Z","timestamp":1426504659000},"page":"1278-1308","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Ricci Curvature, Isoperimetry and a Non-additive Entropy"],"prefix":"10.3390","volume":"17","author":[{"given":"Nikos","family":"Kalogeropoulos","sequence":"first","affiliation":[{"name":"Weill Cornell Medical College in Qatar, Education City, PO Box 24144, Doha, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,16]]},"reference":[{"key":"ref_1","first-page":"30","article-title":"Quantification method of classification processes. 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