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Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
Published on: June 15, 2018
Statistical analysis of complex systems with nonclassical invariant measures.
1PRIMALIGHT, Faculty of Electrical Engineering, Applied Mathematics and Computational Science, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia. andrea.fratalocchi@uniroma1.it
Summary
This study develops a statistical description for complex many-body systems using solitons and the Ablowitz-Kaup-Newell-Segur scheme. It establishes a novel invariant measure and thermodynamics for systems beyond classical ensembles.
Area of Science:
- Statistical Mechanics
- Complex Systems Dynamics
- Nonlinear Physics
Background:
- Classical thermodynamics ensembles struggle to describe complex many-body systems.
- Invariant measures are crucial for statistical descriptions but difficult to construct for certain systems.
Purpose of the Study:
- To develop a method for constructing invariant measures in systems lacking classical thermodynamic ensembles.
- To establish a suitable thermodynamic framework for complex many-body systems, using solitons as a model.
- To explore emergent properties and phase transitions in these systems.
Main Methods:
- Utilized the Ablowitz-Kaup-Newell-Segur (AKNS) scheme for a general formalism.
- Applied the formalism to a one-dimensional phase space model.
- Investigated a universal wave propagation model with gray solitons in a transparent potential.
Main Results:
- Successfully constructed an invariant measure for the complex system.
- Developed a viable thermodynamic framework, including free-energy landscapes.
- Observed rich thermodynamic scenarios with phase transitions and emergent properties.
Conclusions:
- The proposed method enables statistical descriptions for systems intractable by classical ensembles.
- Soliton-based systems exhibit complex thermodynamic behaviors, including controllable emergent properties.
- Identified potential common principles underlying complex dynamics in various fields.
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