Statistical analysis of complex systems with nonclassical invariant measures

Details Statistical analysis of complex systems with nonclassical invariant measures Statistical analysis of complex systems with nonclassical invariant measures

2011-03-08

arxiv.org/abs/1103.1547v1

Phys. Rev. E 83, 021116 (2011)

Nonlinear Sciences

Pattern Formation and Solitons

9 pages, 4 figures

Scientific paper

10.1103/PhysRevE.83.021116

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 such behavior, trying to identify common denominators in the area of complex dynamics.

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