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Relative complexity measures the complexity of a probability preserving transformation relative to a factor being a sequence of random variables whose exponential growth rate is the relative entropy of the extension. We prove distributional…

Dynamical Systems · Mathematics 2012-10-30 Jon Aaronson

Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…

Machine Learning · Statistics 2021-01-13 Yann Issartel

This study explores the role of information entropy in understanding nuclear density distributions, including both stable configurations and non-traditional structures such as neutron halos and $\alpha$-clustering. By quantifying the…

Nuclear Theory · Physics 2024-10-01 Wei-Hu Ma , Yu-Gang Ma

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

Information Theory · Computer Science 2026-03-16 Siang Cheng , Hejun Xu , Tianxiao Pang

The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…

Computational Complexity · Computer Science 2016-05-06 Anatol Slissenko

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…

Chaotic Dynamics · Physics 2009-11-07 G. Boffetta , M. Cencini , M. Falcioni , A. Vulpiani

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…

Statistical Mechanics · Physics 2015-06-18 Torbjørn Helvik , Kristian Lindgren

We compared entropy for texts written in natural languages (English, Spanish) and artificial languages (computer software) based on a simple expression for the entropy as a function of message length and specific word diversity. Code text…

Computation and Language · Computer Science 2015-12-03 Gerardo Febres , Klaus Jaffe , Carlos Gershenson

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

Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…

Probability · Mathematics 2018-06-05 Alison M. Etheridge , Thomas G. Kurtz

We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…

High Energy Physics - Theory · Physics 2025-07-16 Thomas W. Grimm , Mick van Vliet

Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…

Statistical Mechanics · Physics 2022-10-19 Roi Holtzman , Marco Giulini , Raffaello Potestio

In this work, we develop a general method for estimating the Shannon entropy of a bidimensional sequence based on the extrapolation of block entropies. We apply this method to analyse the spatial configurations of cities of different…

Physics and Society · Physics 2024-09-04 E. Brigatti , V. M. Netto , F. N. M. de Sousa Filho , C. Cacholas

The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…

Dynamical Systems · Mathematics 2014-01-14 Marc Harper

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

Information Theory · Computer Science 2012-01-23 Russell K. Standish

Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…

Methodology · Statistics 2017-06-30 Anupam Kundu , Subir Kumar Bhandari

The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…

Quantum Physics · Physics 2025-06-23 Michele Reilly , Seth Lloyd

In this paper, we define a Mathematical model of program structure. Mathematical model of program structure defined here provides unified mathematical treatment of program structure, which reveals that a program is a large and finite set of…

Software Engineering · Computer Science 2014-09-18 Kwangmyong Rim , Yonghua Choe

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…

Quantum Physics · Physics 2025-08-14 Marcos G. Alpino , Tiago Debarba , Reinaldo O. Vianna , André T. Cesário

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