In this paper a non-stationary processes that tend to maximize the Tsallis entropy are considered. Systems with discrete probability distribution for the Tsallis entropy have already been investigated on the basis of the Speed-Gradient principle. The evolution of probability density function and continuous form of the Tsallis entropy are considered. A set of equations describing dynamics of a s...

In this paper, we introduce Nonadditive Information Theory through the axiomatic formulation of Tsallis entropy. We show that systems with transitions from high dimensionality to few degrees of freedom are better described by nonadditive formalism. Such a biological system is the brain and brain rhythms is its macroscopic dynamic trace. We will show with simulations that Tsallis entropy is a po...

Mutual information is one of the mostly used measures for evaluating image similarity. In this paper, we investigate the application of three different Tsallis-based generalizations of mutual information to analyze the similarity between scanned documents. These three generalizations derive from the Kullback–Leibler distance, the difference between entropy and conditional entropy, and the Jense...

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range q in (0, 2]. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists n...

In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.

We prove a tight uniform continuity bound for a family of entropies which includes the von Neumann entropy, the Tsallis entropy and the α-Rényi entropy, Sα, for α ∈ (0, 1). We establish necessary and sufficient conditions for equality in the continuity bound and prove that these conditions are the same for every member of the family. Our result builds on recent work in which we constructed a st...

The conventional coherence is defined with respect to a fixed orthonormal basis, i.e., von Neumann measurement. Recently, generalized quantum general positive operator-valued measurements has been presented. Several well-defined measures, such as the relative entropy of $$C_{r}$$ , $$l_{1}$$ norm $$C_{l_{1}}$$ and $$C_{T,\alpha }$$ based on Tsallis POVMs have obtained. In this work, we investig...

The Tsallis measure of mutual information is combined with the simultaneous perturbation stochastic approximation algorithm to register images. It is shown that Tsallis entropy can improve registration accuracy and speed of convergence, compared with Shannon entropy, in the calculation of mutual information. Simulation results show that the new algorithm achieves up to seven times faster conver...

The purpose of this note is to argue that degree of nonextensivity as given by the Tsallis distribution obtained from maximum entropy principle has a different origin than the nonextensivity inferred from pseudo-additive property of Tsallis entropy. PACS: 05.20.-y, 05.30.-d