Tendency towards maximum complexity in a nonequilibrium isolated system

Calbet, Xavier; López‐Ruiz, Ricardo

doi:10.1103/physreve.63.066116

Cited by 166 publications

(110 citation statements)

References 14 publications

(20 reference statements)

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“…Analogously to the concept of a complexity-entropy plane in nonlinear time series analysis, which has been utilized to discriminate between different types of time series generated by stochastic and deterministic chaotic processes [21,22], we aim to characterize a set of complex networks by means of its average per-node Shannon entropy S and a statistical complexity measure C. We thereby make use of two notions that are related with the complexity of a physical system, namely its information content and its state of disequilibrium [37][38][39]. In particular, we relate the information content of the network with the entropy S and the disequilibrium with the network's Jenson-Shannon divergence Q with respect to an appropriately chosen reference state.…”

Section: Methods and Datamentioning

confidence: 99%

Mapping and discrimination of networks in the complexity-entropy plane

et al. 2017

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Complex networks are usually characterized in terms of their topological, spatial, or informationtheoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here, we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged pernode entropic measure characterizing the network's information content and the associated JensonShannon divergence as a measure of disequilibrium. We study 29 real world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g, transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.

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Section: Methods and Datamentioning

confidence: 99%

Mapping and discrimination of networks in the complexity-entropy plane

et al. 2017

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“…As shown in [13], by mapping out the positions of these systems on the CH plane PE norm × C J S , differing degrees of periodic, chaotic, and stochastic dynamics can be identified. As a functional of the entropy, C J S is constrained between well-defined extremes for a given value of H [30,31]. These crescent-shaped maximum and minimum complexity curves are shown in Fig.…”

Section: Permutation Entropy and The Ch Planementioning

confidence: 99%

Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind

et al. 2015

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. 2015. Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind. Phys. Rev. E 91, 023101.PHYSICAL REVIEW E 91, 023101 (2015) Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind The Bandt-Pompe permutation entropy and the Jensen-Shannon statistical complexity are used to analyze fluctuating time series of three different turbulent plasmas: the magnetohydrodynamic (MHD) turbulence in the plasma wind tunnel of the Swarthmore Spheromak Experiment (SSX), drift-wave turbulence of ion saturation current fluctuations in the edge of the Large Plasma Device (LAPD), and fully developed turbulent magnetic fluctuations of the solar wind taken from the Wind spacecraft. The entropy and complexity values are presented as coordinates on the CH plane for comparison among the different plasma environments and other fluctuation models. The solar wind is found to have the highest permutation entropy and lowest statistical complexity of the three data sets analyzed. Both laboratory data sets have larger values of statistical complexity, suggesting that these systems have fewer degrees of freedom in their fluctuations, with SSX magnetic fluctuations having slightly less complexity than the LAPD edge I sat . The CH plane coordinates are compared to the shape and distribution of a spectral decomposition of the wave forms. These results suggest that fully developed turbulence (solar wind) occupies the lower-right region of the CH plane, and that other plasma systems considered to be turbulent have less permutation entropy and more statistical complexity. This paper presents use of this statistical analysis tool on solar wind plasma, as well as on an MHD turbulent experimental plasma.

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“…In both technical and popular scientific literatures, it is not uncommon to find a "complexity" plotted against entropy in merely schematic form as a sketch of a generic complexity function that vanishes for extreme values of entropy and achieves a maximum in a middle region [5,47,48,49]. Several authors, in fact, have taken these as the only constraints defining complexity [50,51,52,53,54].…”

Section: A Structural Complexitymentioning

confidence: 99%

The organization of intrinsic computation: Complexity-entropy diagrams and the diversity of natural information processing

Feldman

McTague

Crutchfield

2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

145

138

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Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display the range and different kinds of intrinsic computation across an entire class of system. Here, we use complexity-entropy diagrams to analyze intrinsic computation in a broad array of deterministic nonlinear and linear stochastic processes, including maps of the interval, cellular automata and Ising spin systems in one and two dimensions, Markov chains, and probabilistic minimal finite-state machines. Since complexity-entropy diagrams are a function only of observed configurations, they can be used to compare systems without reference to system coordinates or parameters. It has been known for some time that in special cases complexity-entropy diagrams reveal that high degrees of information processing are associated with phase transitions in the underlying process space, the so-called "edge of chaos". Generally, though, complexity-entropy diagrams differ substantially in character, demonstrating a genuine diversity of distinct kinds of intrinsic computation. Discovering organization in the natural world is one of science's central goals. Recent innovations in nonlinear mathematics and physics, in concert with analyses of how dynamical systems store and process information, has produced a growing body of results on quantitative ways to measure natural organization. These efforts had their origin in earlier investigations of the origins of randomness. Eventually, however, it was realized that measures of randomness do not capture the property of organization. This led to the recent efforts to develop measures that are, on the one hand, as generally applicable as the randomness measures but which, on the other, capture a system's complexity-its organization, structure, memory, regularity, symmetry, and pattern. Here-analyzing processes from dynamical systems, statistical mechanics, stochastic processes, and automata theory-we show that measures of structural complexity are a necessary and useful complement to describing natural systems only in terms of their randomness. The result is a broad appreciation of the kinds of information processing embedded in nonlinear systems. This, in turn, * Electronic address:

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Tendency towards maximum complexity in a nonequilibrium isolated system

Cited by 166 publications

References 14 publications

Mapping and discrimination of networks in the complexity-entropy plane

Mapping and discrimination of networks in the complexity-entropy plane

Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind

The organization of intrinsic computation: Complexity-entropy diagrams and the diversity of natural information processing

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