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Complex systems that are characterized by strong correlations and fat-tailed distribution functions have been argued to be incompatible within the framework of Boltzmann-Gibbs entropy. As an alternative, so-called generalized entropies were…

Statistical Mechanics · Physics 2022-08-15 Rudolf Hanel , Stefan Thurner

In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…

Chaotic Dynamics · Physics 2014-07-22 Anton M. Unakafov , Karsten Keller

We address the excess entropy, which is a measure of complexity for stationary time series, from the ordinal point of view. We show that the permutation excess entropy is equal to the mutual information between two adjacent semi-infinite…

Chaotic Dynamics · Physics 2011-12-13 Taichi Haruna , Kohei Nakajima

In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…

Chaotic Dynamics · Physics 2015-03-10 Valentina A. Unakafova , Anton M. Unakafov , Karsten Keller

The deterministic notions of capacity and entropy are studied in the context of communication and storage of information using square-integrable, bandlimited signals subject to perturbation. The $(\epsilon,\delta)$-capacity, that extends…

Information Theory · Computer Science 2015-04-21 Massimo Franceschetti , Taehyung J. Lim

This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…

Physics and Society · Physics 2025-03-27 Yujie Shi , Alex Jie Yang , Sanhong Deng

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…

Quantum Physics · Physics 2017-01-04 Mirjam Weilenmann , Lea Krämer , Philippe Faist , Renato Renner

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

Information Theory · Computer Science 2024-05-07 Mokshay Madiman , Prasad Tetali

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive…

Statistical Mechanics · Physics 2009-10-31 Takuya Yamano

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts…

Logic in Computer Science · Computer Science 2010-10-20 Marie Ferbus-Zanda , Serge Grigorieff

The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…

Neurons and Cognition · Quantitative Biology 2019-06-10 Alberto Hernández-Espinosa , Héctor Zenil , Narsis A. Kiani , Jesper Tegnér

Information is a precise concept that can be defined mathematically, but its relationship to what we call "knowledge" is not always made clear. Furthermore, the concepts "entropy" and "information", while deeply related, are distinct and…

Adaptation and Self-Organizing Systems · Physics 2016-03-03 Christoph Adami

Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…

Machine Learning · Computer Science 2021-03-04 Rishabh Iyer , Ninad Khargonkar , Jeff Bilmes , Himanshu Asnani

Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples…

Computer Vision and Pattern Recognition · Computer Science 2009-05-21 Paul M. B. Vitanyi

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…

Statistical Mechanics · Physics 2019-10-21 Piergiulio Tempesta , Henrik Jeldtoft Jensen

Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…

Data Analysis, Statistics and Probability · Physics 2026-04-20 Andrea Somazzi , Diego Garlaschelli

In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…

Information Theory · Computer Science 2007-07-16 Alexander Shaydurov

Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open…

Computational Complexity · Computer Science 2015-04-28 Omri Weinstein

This paper fills a gap in our understanding of the interaction between information and computation. It unifies other approaches to measuring information like Kolmogorov complexity and Shannon information. We define a theory about…

Information Theory · Computer Science 2016-11-24 P. W. Adriaans

Obtaining meaningful quantitative descriptions of the statistical dependence within multivariate systems is a difficult open problem. Recently, the Partial Information Decomposition (PID) was proposed to decompose mutual information (MI)…

Information Theory · Computer Science 2017-02-21 Robin A. A. Ince