In this paper, we present a generalization of Tsallis relative operator entropy defined for positive operators and investigate some related properties. Some inequalities involving the generalized are pointed out as well.

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Entropy games and matrix multiplication games have been recently introduced by Asarin et al. They model the situation in which one player (Despot) wishes to minimize the growth rate of a matrix product, whereas the other player (Tribune) wishes to maximize it. We develop an operator approach to entropy games. This allows us to show that entropy games can be cast as stochastic mean payoff games ...

J. Fernando Barbero G.,* Jerzy Lewandowski, and Eduardo J. S. Villaseñor Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul. Hoża 69, 00-681 Warsaw, Poland Instituto Gregorio Millán, Grupo de Modelización y Simulación Numérica, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain (R...

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants. We establish the variational principle ...

Kullback–Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one-parameter generalization of Kullback–Leibler relative-entropy in the nonextensive thermostatistics. In this paper, we present the properties of Tsallis relative-entropy minimization and present some differences with the classica...