In this short paper, we establish a variational expression of the Tsallis relative entropy. In addition, we derive a generalized thermodynamic inequality and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized Golden-Thompson inequality.
Matrix inequalities in statistical mechanics
✍ Scribed by N. Bebiano; J. da Providência Jr.; R. Lemos
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 185 KB
- Volume
- 376
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
Some matrix inequalities used in statistical mechanics are presented. A straightforward proof of the Thermodynamic Inequality is given and its equivalence to the Peierls-Bogoliubov inequality is shown.
📜 SIMILAR VOLUMES
Matrix algebra is extensively used in the study of linear models and multivariate analysis (see for instance Refs. [18,21]). During recent years, there have been a number of papers where statistical results are used to prove some matrix theorems, especially matrix inequalities (Refs. [5,7,8,10,14,15
Let A 1 , . . . , A s be nonnegative definite matrices. We prove that there are constants c i , 1 i s, depending on A 1