Ricci curvature, isoperimetry and a non-additive entropy
Abstract
Searching for the dynamical foundations of the Havrda-Charv\'{a}t/Dar\'{o}czy/Cressie-Read/Tsallis non-additive entropy, we come across a covariant quantity called, alternatively, a generalized Ricci curvature, an -Ricci curvature or a Bakry-\'{E}mery-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.
Keywords
Cite
@article{arxiv.1502.05118,
title = {Ricci curvature, isoperimetry and a non-additive entropy},
author = {Nikos Kalogeropoulos},
journal= {arXiv preprint arXiv:1502.05118},
year = {2015}
}
Comments
31 pages, No figures, Standard LaTeX. Based, in part, on a talk delivered at SigmaPhi 2014, 7-11 July 2014, Rhodes, Greece