Related papers: On the average uncertainty for systems with nonlin…
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for…
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…
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
The pathway model of Mathai (2005) mainly deals with the rectangular matrix-variate case. In this paper the scalar version is shown to be associated with a large number of probability models used in physics. Different families of densities…
When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total…
Though Shannon entropy of a probability measure $P$, defined as $- \int_{X} \frac{\ud P}{\ud \mu} \ln \frac{\ud P}{\ud\mu} \ud \mu$ on a measure space $(X, \mathfrak{M},\mu)$, does not qualify itself as an information measure (it is not a…
This paper proposes a new method for estimating the joint probability mass function of a pair of discrete random variables. This estimator is used to construct joint Shannon R\'enyi-Tsallis entropies, and the mutual information estimates of…
In the nonextensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
This research paper delves into the innovative integration of Shannon entropy and rough set theory, presenting a novel approach to generalize the evaluation approach in machine learning. The conventional application of entropy, primarily…
In this work, we define a family of probability densities involving the generalized trigonometric functions defined by Dr\'abek and Man\'asevich [1], which we name Generalized Trigonometric Densities. We show their relationship with the…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this letter, we introduce a systematic method to construct a series of entropies,…