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arXiv · 1502.05118

Ricci curvature, isoperimetry and a non-additive entropy

Nikos Kalogeropoulos
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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 $N$-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.

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Nikos Kalogeropoulos. 2015-02-18. Ricci curvature, isoperimetry and a non-additive entropy. https://doi.org/10.3390/e17031278

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