Statistical analysis of complex systems with nonclassical invariant measures
KAUST DepartmentPRIMALIGHT Research Group
Electrical Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractI 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.
CitationStatistical analysis of complex systems with nonclassical invariant measures 2011, 83 (2) Physical Review E
PublisherAmerican Physical Society (APS)
JournalPhysical Review E
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