Statistical analysis of complex systems with nonclassical invariant measures
Type
ArticleAuthors
Fratalocchi, Andrea
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
PRIMALIGHT Research Group
Physical Science and Engineering (PSE) Division
Date
2011-02-28Preprint Posting Date
2011-03-08Permanent link to this record
http://hdl.handle.net/10754/552985
Metadata
Show full item recordAbstract
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 EPublisher
American Physical Society (APS)Journal
Physical Review EPubMed ID
21405827arXiv
1103.1547ae974a485f413a2113503eed53cd6c53
10.1103/PhysRevE.83.021116
Scopus Count
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