Peierls–Bogolyubov’s Inequality for Deformed Exponentials
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-06-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/19/6/271 |
| _version_ | 1828371627622006784 |
|---|---|
| author | Frank Hansen Jin Liang Guanghua Shi |
| author_facet | Frank Hansen Jin Liang Guanghua Shi |
| author_sort | Frank Hansen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T06:51:57Z |
| format | Article |
| id | doaj.art-f9c92f7fa008471ca2f36a8b90ce119f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T06:51:57Z |
| publishDate | 2017-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f9c92f7fa008471ca2f36a8b90ce119f2022-12-22T02:07:01ZengMDPI AGEntropy1099-43002017-06-0119627110.3390/e19060271e19060271Peierls–Bogolyubov’s Inequality for Deformed ExponentialsFrank Hansen0Jin Liang1Guanghua Shi2Institute for Excellence in Higher Education, Tohoku University, Sendai 980-8576, JapanSchool of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, ChinaSchool of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, ChinaWe 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.http://www.mdpi.com/1099-4300/19/6/271deformed exponential functionPeierls–Bogolyubov’s inequalityTsallis relative entropy |
| spellingShingle | Frank Hansen Jin Liang Guanghua Shi Peierls–Bogolyubov’s Inequality for Deformed Exponentials Entropy deformed exponential function Peierls–Bogolyubov’s inequality Tsallis relative entropy |
| title | Peierls–Bogolyubov’s Inequality for Deformed Exponentials |
| title_full | Peierls–Bogolyubov’s Inequality for Deformed Exponentials |
| title_fullStr | Peierls–Bogolyubov’s Inequality for Deformed Exponentials |
| title_full_unstemmed | Peierls–Bogolyubov’s Inequality for Deformed Exponentials |
| title_short | Peierls–Bogolyubov’s Inequality for Deformed Exponentials |
| title_sort | peierls bogolyubov s inequality for deformed exponentials |
| topic | deformed exponential function Peierls–Bogolyubov’s inequality Tsallis relative entropy |
| url | http://www.mdpi.com/1099-4300/19/6/271 |
| work_keys_str_mv | AT frankhansen peierlsbogolyubovsinequalityfordeformedexponentials AT jinliang peierlsbogolyubovsinequalityfordeformedexponentials AT guanghuashi peierlsbogolyubovsinequalityfordeformedexponentials |