Ricci Curvature, Isoperimetry and a Non-additive Entropy

Entropy

Nikos Kalogeropoulos¹ 

[1] Weill Cornell Medical College in Qatar, Education City, PO Box 24144, Doha, Qatar; E-Mail

关键词: non-extensive entropy;    Bakry-Émery-Ricci tensor;    optimal transport;    isoperimetric inequalities;   

DOI  :  10.3390/e17031278

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland