Related papers: Example of a possible interpretation of Tsallis en…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop…
The maximum entropy principle is often used for bi-level or multi-level thresholding of images. For this purpose, some methods are available based on Shannon and Tsallis entropies. In this paper, we discuss them and propose a method based…
How complex of the complex networks has attracted many researchers to explore it. The entropy is an useful method to describe the degree of the $complex$ of the complex networks. In this paper, a new method which is based on the Tsallis…
We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty…
Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In…
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon…
The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under…
In a recent paper [Entropy 2020, 22(1), 17] C. Tsallis states that entropy -- as in Shannon's or Kullback-Leiber's definitions -- is inadequate to interpret black hole entropy and suggests that a new non-additive functional should take the…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…
The notion of entropy penetrates much of science. A key feature of the all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity (additivity over independent subsystems). However, there is a need for other quantities. In…
We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence $S(x)$. We establish recurrence…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
We present a path toward determining the statistical origin of the thermodynamic limit for systems with long-range interactions. We assume throughout that the systems under consideration have thermodynamic properties given by the Tsallis…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy…
In this simple article, with possible applications in theoretical and applied physics, we suggest an original way to derive the expression of Shannon's entropy from a purely variational approach,using constraints. Based on the work of Edwin…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…