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...

In this communication, order preserving property of Tsallis measure of entropy is proved. Further, subdditivity and submodularity of Tsallis measure of entropy on a majorization are established. Additionally, Shannon’s [11] little-recognized legacy, an interesting concepts of information elements and information lattices is studied.

The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev’s axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin’s axiom in [7], in the sence that our axiom is simpler than his one, as similar that Faddeev’s axiom is simpler than Shannon-Khinchin’s one.

We consider the generalized differential entropy of normalized sums of independent and identically distributed (IID) continuous random variables. We prove that the Rényi entropy and Tsallis entropy of order α (α > 0) of the normalized sum of IID continuous random variables with bounded moments are convergent to the corresponding Rényi entropy and Tsallis entropy of the Gaussian limit, and obtai...

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

Water engineering is an amalgam of engineering (e.g., hydraulics, hydrology, irrigation, ecosystems, environment, water resources) and non-engineering (e.g., social, economic, political) aspects that are needed for planning, designing and managing water systems. These aspects and the associated issues have been dealt with in the literature using different techniques that are based on different ...

In this research paper, it is proved that an approximation to Gibbs-Shannon entropy measure naturally leads to Tsallis entropy for the real parameter q =2 . Several interesting measures based on the input as well as output of a discrete memoryless channel are provided and some of the properties of those measures are discussed. It is expected that these results will be of utility in Information ...