A review of the mathematical properties of the Tsallis entropies

作     者：Furuichi, Shigeru furuichi@cssa.chs.nihon-u.ac.jp 

作者机构：Department of Computer Science and System Analysis College of Humanities and Sciences Nihon University 3-25-40 Sakurajosui Setagaya-ku Tokyo Japan 

出 版 物：《AIP Conference Proceedings》 (美国物理学会会议录)

年 卷 期：2008年第1045卷第1期

页      面：11-20页

学科分类：07[理学] 0702[理学-物理学] 

主　　题：enanglement and quantum information theory Fannes' inequality Matrix trace inequalities maximum entropy principle Tsallis relative entropy variational expression 

摘      要：We review the mathematical properties of the generalized entropies, based on our previous papers. This review is an extended version of our article [9]. The Tsallis entropy defined for a quantum state is uniquely derived from three axioms. A generalized Fannes’ inequality is shown. The maximum entropy principle in Tsallis statistics are revisited as an application of the Tsallis relative entropy defined for nonnegative matrices in the framework of matrix analysis. A variational expression for Tsallis relative entropy is derived and some related inequalities are studied. Finally, an application to qunatum information theory is discussed. [ABSTRACT FROM AUTHOR]