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    Statistical analysis of complex systems with nonclassical invariant measures

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    PhysRevE.83.021116.pdf
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    Description:
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    Type
    Article
    Authors
    Fratalocchi, Andrea cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    PRIMALIGHT Research Group
    Physical Science and Engineering (PSE) Division
    Date
    2011-02-28
    Preprint Posting Date
    2011-03-08
    Permanent link to this record
    http://hdl.handle.net/10754/552985
    
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    Abstract
    I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a general formalism based on the Ablowitz-Kaup-Newell-Segur scheme, I demonstrate how to build an invariant measure and, within a one-dimensional phase space, how to develop a suitable thermodynamics. A detailed example is provided with a universal model of wave propagation, with reference to a transparent potential sustaining gray solitons. The system shows a rich thermodynamic scenario, with a free-energy landscape supporting phase transitions and controllable emergent properties. I finally discuss the origin of such behavior, trying to identify common denominators in the area of complex dynamics.
    Citation
    Statistical analysis of complex systems with nonclassical invariant measures 2011, 83 (2) Physical Review E
    Publisher
    American Physical Society (APS)
    Journal
    Physical Review E
    DOI
    10.1103/PhysRevE.83.021116
    PubMed ID
    21405827
    arXiv
    1103.1547
    Additional Links
    http://link.aps.org/doi/10.1103/PhysRevE.83.021116
    http://arxiv.org/abs/1103.1547
    ae974a485f413a2113503eed53cd6c53
    10.1103/PhysRevE.83.021116
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; PRIMALIGHT Research Group; Electrical and Computer Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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