The proper way of averaging is an important question with regards to Tsal-lis' Thermostatistics. Three different procedures have been thus far employed in the pertinent literature. The third one, i.e., the Tsallis-Mendes-Plastino (TMP) [1] normalization procedure, exhibits clear advantages with respect to earlier ones. In this work, we advance a distinct (from the TMP-one) way of handling the L...

It has been recently shown that the Bekenstein entropy bound is not respected by systems satisfying modified forms of Heisenberg uncertainty principle (HUP) including generalized and extended principles, or even their combinations. On other, use entropies, which differ from entropy, in describing gravity related topics signals us to different equipartition expressions compared usual one. In way...

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 ...

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...

It is demonstrated clearly that for the same classic generalized system the Tsallis power-laws with both the 1 > q and the 1 < q can be induced by the constraint of the constant harmonic mean for the so-called reciprocal energies r E and at the same time the Boltzmann distribution or the negative exponential probability distribution can be generated with the constraint of the constant arithmeti...

A systematic analysis of transverse momentum and rapidity distributions measured in high-energy proton proton (pp) collisions for energies ranging from 53 GeV to 7 TeV using Tsallis thermodynamics is presented. The excellent description of all transverse momentum spectra obtained in earlier analyses is confirmed and extended. All energies can be described by a single Tsallis temperature of 68 ±...

From the Tsallis unnormalized (or Tsallis-2) statistical mechanical formulation, B\"{u}y\"{u}kkili\c{c} {\it et al.} [Phys. Lett. A 197, 209 (1995)] derived expressions for single-particle distribution functions (known as phenomenological distributions) particles obeying Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics using factorization approximation. In spite of fact that this pap...

Monogamy and polygamy relations characterize the quantum correlation distributions among multipartite systems. We investigate monogamy satisfied by measures of general correlation. By using Hamming weight, we derive new inequalities $\beta$-th power $\alpha$-th correlations, respectively. show that these are tighter than existing ones, such as [Int. J. Theor. Phys. 60, 1455-1470 (2021)]. Taking...

Entropy based measures have been frequently used in symbolic sequence analysis. A symmetrized and smoothed form of Kullback-Leibler divergence or relative entropy, the Jensen-Shannon divergence (JSD), is of particular interest because of its sharing properties with families of other divergence measures and its interpretability in different domains including statistical physics, information theo...

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...