Results 1 to 10 of about 130 (87)
A Unified Framework Linking Entropy, Fractal Dimension, and Lyapunov Exponents in Chaotic Dynamics
ComplexityThis study presents a universal operator framework predicting critical transitions in nonlinear systems through the intrinsic nexus of entropy, fractal geometry, and chaos.
Elio Quiroga Rodríguez
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Generalized Ordinal Patterns and the KS-Entropy
Entropy, 2021 Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G.
Tim Gutjahr, Karsten Keller
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Observational Modeling of the Kolmogorov-Sinai Entropy [PDF]
Sahand Communications in Mathematical Analysis, 2019 In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then the ergodic properties of relative semi-dynamical ...
Uosef Mohammadi
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Ordinal Pattern Based Entropies and the Kolmogorov–Sinai Entropy: An Update
Entropy, 2020 Different authors have shown strong relationships between ordinal pattern based entropies and the Kolmogorov−Sinai entropy, including equality of the latter one and the permutation entropy, the whole picture is however far from being complete. This
Tim Gutjahr, Karsten Keller
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Entropy, 2021 Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers.
Tim Gutjahr, Karsten Keller
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Quantum Kolmogorov-Sinai entropy and Pesin relation
Physical Review Research, 2021 We discuss a quantum Kolmogorov-Sinai entropy defined as the entropy production per unit time resulting from coupling the system to a weak, auxiliary bath.
Tomer Goldfriend, Jorge Kurchan
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Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum
Journal of High Energy Physics, 2022 In classical chaotic systems the entropy, averaged over initial phase space distributions, follows a universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the Kolmogorov-Sinai ...
Georg Maier +2 more
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On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies
Entropy, 2014 We consider the concept of generalized Kolmogorov–Sinai entropy, where instead of the Shannon entropy function, we consider an arbitrary concave function defined on the unit interval, vanishing in the origin.
Fryderyk Falniowski
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Logical entropy of dynamical systems
Advances in Difference Equations, 2018 The main purpose of the paper is to extend the results of Ellerman (Int. J. Semant. Comput. 7:121–145, 2013) to the case of dynamical systems. We define the logical entropy and conditional logical entropy of finite measurable partitions and derive the ...
Dagmar Markechová +2 more
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ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES
Forum of Mathematics, Sigma, 2016 Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov–Sinai entropy from the setting of amenable groups.
TIM AUSTIN
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