It is often stated that heat baths with finite degrees of freedom i.e., finite baths, are sources of Tsallis distributions for classical Hamiltonian systems. By using well-known fundamental statistical mechanics expressions, we rigorously show that Tsallis distributions with fat tails are possible only for finite baths with constant negative heat capacity, while constant positive heat capacity ...

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...

We derive a dual-primal recursive algorithm based on the Fenchel duality framework, extending Dykstra’s successive projections and Csiszar’s I-projections schemes, to handle Tsallis MaxEnt. The Tsallis entropy Sq(p) is a one-parameter extension of Shannon’s entropyH(p) in the sense that Sq→1(p) = H(p). The solution of the Tsallis MaxEnt falls under a q-deformed Gibbs distribution which is a pow...

This paper studies the use of the Tsallis Entropy versus the classic BoltzmannGibbs-Shannon entropy for classifying image patterns. Given a database of 40 pattern classes, the goal is to determine the class of a given image sample. Our experiments show that the Tsallis entropy encoded in a feature vector for different q indices has great advantage over the Boltzmann-Gibbs-Shannon entropy for pa...

The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the channel capacity by maximization of the Tsallis entropy within a given condition of code length. As a result, we obtained a simple relational expression betw...

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 uniqueness theorem for the relative entropy was proven by A.Hobson. Recently, the Tsallis entropy was characterized by H.Suyari in terms of the generalized ShannonKhinchin’s axiom. In this short paper, we characterize the Tsallis relative entropy in the finite discrete system by generalizing the conditions in Hobson’s axiom.

We revisit recent derivations of kinetic equations based on Tsallis' entropy concept. The method of kinetic functions is introduced as a standard tool for extensions of classical kinetic equations in the framework of Tsallis' statistical mechanics. Our analysis of the Boltzmann equation demonstrates a remarkable relation between thermodynamics and kinetics caused by the deformation of macroscop...

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.

We shall show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that the Tsallis entropy function is characterized by a functional equation, which is a different form used in [1] i.e., in Proposition 2.1 in the present paper. We also give an interpretation of the functional equation giving the Tsallis entropy funct...