Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving co...

The connection between Tsallis entropy for a multifractal distribution and Jackson’s q-derivative is established. Based on this derivation and definition of a homogeneous function, a q-analogue of Shannon’s entropy is discussed. q-additivity of this entropy is shown. We also define q-analogue of Kullback relative entropy. The implications of lattice structure beneath q-calculus are highlighted ...

Equilibrium or meta-equilibrium incomplete thermostatistics with different q indices Abstract We discuss a possibility of establishing a nonextensive incomplete statistics based on Tsallis entropy for equilibrium systems with different q values.

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for ...

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 ...

The Tsallis entropy, as a generalization of the standard Shannon-type entropy, was introduced by Constantino Tsallis (1988). Since that the concept has been extensively studied (see, e.g., Tsallis (2009)). In the present paper we address the problem of generalizing the concept for infinitedimensional systems, i.e., the random processes and fields. Apparently, rather well suited models are the G...

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...

This article investigates a novel automatic microcalcification detection method using a type II fuzzy index. The thresholding is performed using the Tsallis entropy characterized by another parameter ‘q’, which depends on the non-extensiveness of a mammogram. In previous studies, ‘q’ was calculated using the histogram distribution, which can lead to erroneous results when pectoral muscles are i...

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.