A mathematical review of the generalized entropies and their matrix trace inequalities
نویسنده
چکیده
We review the properties of the generalized entropies in our previous papers in the following way. (1)A generalized Fannes’ inequality is shown by the axiomatically characterized Tsallis entropy. (2)The maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for the nonnegative matrices in the framework of matrix analysis. (3)A variational expression for Tsallis relative entropy is derived and some related inequalities are studied. Matrix trace inequalities, Tsallis relative entropy, Fannes’ inequality, variational expression and maximum entropy principle
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Matrix Trace Inequalities on the Tsallis Entropies
Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addition, some matrix trace inequalities related to the Tsallis relative entropy are studied.
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