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Open AccessArticle

Peierls–Bogolyubov’s Inequality for Deformed Exponentials

by Frank Hansen 1,*,†, Jin Liang 2,† and Guanghua Shi 2,†
Institute for Excellence in Higher Education, Tohoku University, Sendai 980-8576, Japan
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Antonio M. Scarfone
Entropy 2017, 19(6), 271;
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)
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
MDPI and ACS Style

Hansen, F.; Liang, J.; Shi, G. Peierls–Bogolyubov’s Inequality for Deformed Exponentials. Entropy 2017, 19, 271.

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