{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T00:26:49Z","timestamp":1778372809577,"version":"3.51.4"},"reference-count":11,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,6,12]],"date-time":"2017-06-12T00:00:00Z","timestamp":1497225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2013Bogolyubov\u2019s inequality. We use these results to improve previously-known lower bounds for the Tsallis relative entropy.<\/jats:p>","DOI":"10.3390\/e19060271","type":"journal-article","created":{"date-parts":[[2017,6,12]],"date-time":"2017-06-12T10:27:59Z","timestamp":1497263279000},"page":"271","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Peierls\u2013Bogolyubov\u2019s Inequality for Deformed Exponentials"],"prefix":"10.3390","volume":"19","author":[{"given":"Frank","family":"Hansen","sequence":"first","affiliation":[{"name":"Institute for Excellence in Higher Education, Tohoku University, Sendai 980-8576, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghua","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/j.laa.2006.03.015","article-title":"Trace inequalities in non-extensive statistical mechanics","volume":"418","author":"Furuichi","year":"2006","journal-title":"Linear Algebra Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1007\/s10955-015-1237-6","article-title":"Golden-Thompson\u2019s inequality for deformed exponentials","volume":"159","author":"Hansen","year":"2015","journal-title":"J. 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