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Entropy 2015, 17(3), 1278-1308; doi:10.3390/e17031278

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
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)
View Full-Text   |   Download PDF [315 KB, uploaded 16 March 2015]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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

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