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Related papers: Entropy Measures vs. Algorithmic Information

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A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…

Statistical Mechanics · Physics 2010-08-18 B. N. Tiwari , Vinod Chandra , Subhashish Banerjee

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…

Statistics Theory · Mathematics 2023-06-02 Guillaume Dulac , Thomas Simon

We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed `assembly index' that belongs to the LZ family of popular compression algorithms (ZIP,…

Information Theory · Computer Science 2024-04-04 Felipe S. Abrahão , Santiago Hernández-Orozco , Narsis A. Kiani , Jesper Tegnér , Hector Zenil

The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and…

Statistical Mechanics · Physics 2009-11-11 A. M. Mathai , H. J. Haubold

Adjusted for chance measures are widely used to compare partitions/clusterings of the same data set. In particular, the Adjusted Rand Index (ARI) based on pair-counting, and the Adjusted Mutual Information (AMI) based on Shannon information…

Machine Learning · Statistics 2015-12-07 Simone Romano , Nguyen Xuan Vinh , James Bailey , Karin Verspoor

We quantify a social organization's potentiality, that is its ability to attain different configurations. The organization is represented as a network in which nodes correspond to individuals and (multi-)edges to their multiple…

Physics and Society · Physics 2019-09-18 Christian Zingg , Giona Casiraghi , Giacomo Vaccario , Frank Schweitzer

The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits,…

Information Theory · Computer Science 2026-01-01 Jianfeng Xu , Zeyan Li

We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…

Quantum Physics · Physics 2007-05-23 C. G. Chakrabarti , Indranil Chakrabarty

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…

Information Theory · Computer Science 2013-05-15 Marek Śmieja

In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…

Information Theory · Computer Science 2017-07-12 Hector Zenil , Narsis Kiani , Jesper Tegnér

Researchers have proposed formal definitions of quantitative information flow based on information theoretic notions such as the Shannon entropy, the min entropy, the guessing entropy, and channel capacity. This paper investigates the…

Cryptography and Security · Computer Science 2010-04-02 Hirotoshi Yasuoka , Tachio Terauchi

The entropy of probability distribution defined by Shannon has several extensions. R\'enyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum…

Mathematical Physics · Physics 2019-09-04 Farrukh Mukhamedov , Kyouhei Ohmura , Noboru Watanabe

Shannon entropy ($S$), R{\'e}nyi entropy ($R$), Tsallis entropy ($T$), Fisher information ($I$) and Onicescu energy ($E$) have been explored extensively in both \emph{free} H atom (FHA) and \emph{confined} H atom (CHA). For a given quantum…

Quantum Physics · Physics 2019-04-05 Neetik Mukherjee , Amlan K. Roy

The Tsallis entropy given for a positive parameter $\alpha$ can be considered as a modification of the classical Shannon entropy. For the latter, corresponding to $\alpha=1$, there exist many axiomatic characterizations. One of them based…

Mathematical Physics · Physics 2017-04-27 Sonja Jäckle , Karsten Keller

Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…

Chaotic Dynamics · Physics 2009-11-10 Milan Rajkovic

Choice overload occurs when individuals feel overwhelmed by an excessive number of options. Experimental evidence suggests that a larger selection can complicate the decision-making process. Consequently, choice satisfaction may diminish…

Physics and Society · Physics 2024-12-18 Mojtaba Madadi Asl , Kamal Hajian , Rouzbeh Torabi , Mehdi Sadeghi

We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…

Computational Geometry · Computer Science 2025-08-29 David Eppstein , Michael T. Goodrich , Abraham M. Illickan , Claire A. To

Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…

Quantum Physics · Physics 2026-04-08 Johannes Jakob Meyer , Asad Raza , Jacopo Rizzo , Lorenzo Leone , Sofiene Jerbi , Jens Eisert

Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space…

Quantum Physics · Physics 2026-04-21 Weijun Feng , Yongzhen Xu , Lvzhou Li , Gongde Guo , Song Lin

Shannon entropy is not the only entropy that is relevant to machine-learning datasets, nor possibly even the most important one. Traditional entropies such as Shannon entropy capture information represented by elements' frequencies but not…

Information Theory · Computer Science 2026-04-01 Phuc Nguyen , Josiah Couch , Rahul Bansal , Alexandra Morgan , Chris Tam , Miao Li , Rima Arnaout , Ramy Arnaout