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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…

Quantum Physics · Physics 2015-07-21 Chien-Hao Lin , Yew Kam Ho

Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…

Probability · Mathematics 2025-03-21 Naveen Kumar , Ambesh Dixit , Vivek Vijay

The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…

Information Theory · Computer Science 2026-03-04 E. P. Csirmaz , L. Csirmaz

We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…

Information Theory · Computer Science 2010-10-21 Oliver Johnson , Yaming Yu

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

Information Theory · Computer Science 2011-04-05 Paul M. B. Vitányi

The Shannon lower bound is one of the few lower bounds on the rate-distortion function that holds for a large class of sources. In this paper, it is demonstrated that its gap to the rate-distortion function vanishes as the allowed…

Information Theory · Computer Science 2016-11-17 Tobias Koch

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…

chao-dyn · Physics 2009-10-30 Stefano Lepri , Antonio Politi , Alessandro Torcini

Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…

Statistics Theory · Mathematics 2019-01-31 Salah H. Abid , Uday J. Quaez

In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…

Information Theory · Computer Science 2020-08-13 Mladen Kovačević , Ivan Stanojević , Vojin Šenk

The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…

Statistics Theory · Mathematics 2013-03-08 David Källberg , Nikolaj Leonenko , Oleg Seleznjev

We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…

Dynamical Systems · Mathematics 2013-09-25 Fryderyk Falniowski

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…

Statistics Theory · Mathematics 2025-07-21 Konstantinos Zografos

Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the Von…

Disordered Systems and Neural Networks · Physics 2011-09-30 Kartik Anand , Ginestra Bianconi , Simone Severini

We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…

Information Theory · Computer Science 2022-12-27 Doron Cohen , Aryeh Kontorovich , Aaron Koolyk , Geoffrey Wolfer

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…

Statistical Mechanics · Physics 2017-09-13 S. E. Marzen , J. P. Crutchfield

The paper examines relationships between the conditional Shannon entropy and the expectation of $\ell_{\alpha}$-norm for joint probability distributions. More precisely, we investigate the tight bounds of the expectation of…

Information Theory · Computer Science 2020-08-24 Yuta Sakai , Ken-ichi Iwata

This paper is prepared as a contribution to the proceedings after the 12th ICSSUR/Feynfest Conference held in Foz do Iguacu (Brazil) from 2 to 6 May 2011. In the first part I briefy report the topic of entropic uncertainty relations for…

Quantum Physics · Physics 2011-09-29 Łukasz Rudnicki

This paper studies the problem of estimating the differential entropy $h(S+Z)$, where $S$ and $Z$ are independent $d$-dimensional random variables with $Z\sim\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$. The distribution of $S$ is unknown, but $n$…

Statistics Theory · Mathematics 2019-06-04 Ziv Goldfeld , Kristjan Greenewald , Yury Polyanskiy

Non Performing Asset(NPA) has been in a serious attention by banks over the past few years. NPA cause a huge loss to the banks hence it becomes an extremely critical step in deciding which loans have the capabilities to become an NPA and…

Machine Learning · Computer Science 2020-05-01 Ambarish Moharil , Nikhil Sonavane , Chirag Kedia , Mansimran Singh Anand

The paper examines relationships between the Shannon entropy and the $\ell_{\alpha}$-norm for $n$-ary probability vectors, $n \ge 2$. More precisely, we investigate the tight bounds of the $\ell_{\alpha}$-norm with a fixed Shannon entropy,…

Information Theory · Computer Science 2016-01-29 Yuta Sakai , Ken-ichi Iwata