Related papers: A two-parameter entropy and its fundamental proper…
Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the R\'{e}nyi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
This paper studies the use of the Tsallis Entropy versus the classic Boltzmann-Gibbs-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…
It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability and the axiomatic foundation.
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
This paper derives bounds for two omnipresent information theoretic measures, the Shannon entropy and its complementary dual, the extropy. Based on a large size data set from a logconcave model, the said bounds are obtained for the entropy…
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…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
We propose an entropy-based information measure, namely the Discounted Least Information Theory of Entropy (DLITE), which not only exhibits important characteristics expected as an information measure but also satisfies conditions of a…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs--Shannon entropy into more general framework - Renyi's information entropy. We address the…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…
The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that…
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…
Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential…
In this paper, we investigate two-parameter entropies and obtain some conditions for their extensivity. By using a generalized $(k,r)-product$, correlations for subsystems are related to the joint probabilities, so that the entropy remains…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This…