Fundamental properties of Tsallis relative entropy

Details Fundamental properties of Tsallis relative entropy Fundamental properties of Tsallis relative entropy

2004-06-08

arxiv.org/abs/cond-mat/0406178v5

J.Math.Phys.,Vol.45,Issue 12, pp. 4868-4877(2004)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1063/1.1805729

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible. The generalized Tsallis relative entropy is defined and its subadditivity is shown by its joint convexity. Moreover, the generalized Peierls-Bogoliubov inequality is also proven.

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