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Open AccessArticle

Ricci Curvature, Isoperimetry and a Non-additive Entropy

Weill Cornell Medical College in Qatar, Education City, PO Box 24144, Doha, Qatar
Academic Editor: Giorgio Kaniadakis
Entropy 2015, 17(3), 1278-1308; https://doi.org/10.3390/e17031278
Received: 12 February 2015 / Revised: 10 March 2015 / Accepted: 11 March 2015 / Published: 16 March 2015
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
Searching for the dynamical foundations of Havrda-Charvát/Daróczy/ 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-Émery-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. View Full-Text
Keywords: non-extensive entropy; Bakry-Émery-Ricci tensor; optimal transport; isoperimetric inequalities non-extensive entropy; Bakry-Émery-Ricci tensor; optimal transport; isoperimetric inequalities
MDPI and ACS Style

Kalogeropoulos, N. Ricci Curvature, Isoperimetry and a Non-additive Entropy. Entropy 2015, 17, 1278-1308.

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