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A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…

Information Theory · Computer Science 2025-01-22 Zsolt Pocze

Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…

Information Theory · Computer Science 2023-04-26 Arthur Jun Zhang

Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…

General Physics · Physics 2017-07-13 Kiyam Lin , SongLing Lin

Information theory is introduced in this lecture note with a particular emphasis on its relevance to algebraic coding theory. The document develops the mathematical foundations for quantifying uncertainty and information transmission by…

Information Theory · Computer Science 2025-12-08 El Mahdi Mouloua , Essaid Mohamed

The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…

Computation · Statistics 2017-10-11 Brendon J. Brewer

Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…

Quantum Physics · Physics 2023-05-30 Alexey E. Rastegin

It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…

Statistical Mechanics · Physics 2012-09-26 Phil Attard

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

Information Theory · Computer Science 2022-05-30 Kenneth Bogert

Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…

Neurons and Cognition · Quantitative Biology 2015-01-09 Robin A. A. Ince , Stefano Panzeri , Simon R. Schultz

This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three…

Statistical Mechanics · Physics 2007-07-13 Robert K. Niven

This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…

Information Theory · Computer Science 2024-10-30 Yilun Liu , Lidong Zhu

In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…

Dynamical Systems · Mathematics 2019-08-17 Vieri Benci , Claudio Bonanno , Stefano Galatolo , Giulia Menconi , Federico Ponchio

This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…

Information Theory · Computer Science 2021-04-26 Ricky X. F. Chen

Information Theory concepts and methodologies conform the background of how communication systems are studied and understood. They are mainly focused on the source-channel-receiver problem and on the asymptotic limits of accuracy and…

Adaptation and Self-Organizing Systems · Physics 2017-05-16 Nicolás Rubido , Celso Grebogi , Murilo S. Baptista

The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…

Quantum Physics · Physics 2014-02-26 Patrick J. Coles , Marco Piani

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

We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…

Quantitative Methods · Quantitative Biology 2007-07-13 Ilya Nemenman

We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…

Information Theory · Computer Science 2022-08-29 Francis Bach

A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the…

Information Theory · Computer Science 2009-09-29 Henryk Borowczyk

The authors discuss information-based complexity theory, which is a model of finite-precision computations with real numbers, and its applications to numerical analysis.

Numerical Analysis · Mathematics 2008-02-03 J. F. Traub , Henryk Woźniakowski