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    Principal Research Fellow

    CSIRO ICT Centre, Sydney

    Relating Fisher Information to Order Parameters

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    We study phase transitions and relevant order parameters via statistical estimation theory using the Fisher information matrix. The assumptions that we make limit our analysis to order parameters representable as a negative derivative of thermodynamic potential over some thermodynamic variable. Nevertheless, the resulting representation is sufficiently general and explicitly relates elements of the Fisher information matrix to the rate of change in the corresponding order parameters. The obtained relationships allow us to identify, in particular, second-order phase transitions via divergences of individual elements of the Fisher information matrix. A computational study of random Boolean networks (RBNs) supports the derived relationships, illustrating that Fisher information of the magnetization bias (that is, activity level) is peaked in nite-size networks at the critical points, and the maxima increase with the network size. The framework presented here reveals the basic thermodynamic reasons behind similar empirical observations reported previously. The study highlights the generality of Fisher information as a measure that can be applied to a broad range of systems, particularly those where the determination of order parameters is cumbersome.

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    Description

    Title : Relating Fisher Information to Order Parameters
    Author(s) : Mikhail Prokopenko, Joseph T. Lizier, Oliver Obst, and X. Rosalind Wang
    Abstract : We study phase transitions and relevant order parameters via statistical estimation theory using the Fisher information matrix. The assumptions that we make limit our analysis to order parameters representable as a negative derivative of thermodynamic potential over some thermodynamic variable. Nevertheless, the resulting representation is sufficiently general and explicitly relates elements of the Fisher information matrix to the rate of change in the corresponding order parameters. The obtained relationships allow us to identify, in particular, second-order phase transitions via divergences of individual elements of the Fisher information matrix. A computational study of random Boolean networks (RBNs) supports the derived relationships, illustrating that Fisher information of the magnetization bias (that is, activity level) is peaked in nite-size networks at the critical points, and the maxima increase with the network size. The framework presented here reveals the basic thermodynamic reasons behind similar empirical observations reported previously. The study highlights the generality of Fisher information as a measure that can be applied to a broad range of systems, particularly those where the determination of order parameters is cumbersome.
    Keywords : phase transitions, order parameters, Fisher information, statistical mechanics, random Boolean networks

    Subject : Fisher information and order parameters
    Area : Computer Science
    Language : English
    Year : 2011

    Affiliations CSIRO ICT Centre, Sydney
    Journal : Physical Review E
    Volume : 84
    Pages : 041116
    Attribution Non-Commercial No Derivatives

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    Mikhail's Peer Evaluation activity

    Downloads 490
    Views 97
    Followed by 1
    • Gloria Origgi, Research Fellow, CNRS, Institut Nicod, Ecole Normale Supérieure, Ecole des Hautes Etudes, Paris.

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