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Entropy 2017, 19(6), 271;

Peierls–Bogolyubov’s Inequality for Deformed Exponentials

1,†,* , 2,†
Institute for Excellence in Higher Education, Tohoku University, Sendai 980-8576, Japan
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editor: Antonio M. Scarfone
Received: 14 April 2017 / Revised: 2 June 2017 / Accepted: 5 June 2017 / Published: 12 June 2017
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
Full-Text   |   PDF [243 KB, uploaded 14 June 2017]


We study the convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and in this way obtain new trace inequalities for deformed exponentials that may be considered as generalizations of Peierls–Bogolyubov’s inequality. We use these results to improve previously-known lower bounds for the Tsallis relative entropy. View Full-Text
Keywords: deformed exponential function; Peierls–Bogolyubov’s inequality; Tsallis relative entropy deformed exponential function; Peierls–Bogolyubov’s inequality; Tsallis relative entropy
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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Hansen, F.; Liang, J.; Shi, G. Peierls–Bogolyubov’s Inequality for Deformed Exponentials. Entropy 2017, 19, 271.

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