Permutation entropy for the characterization of the attractive Hamiltonian mean-field model
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Summary
This summary is machine-generated.The Hamiltonian mean-field model
Area Of Science
- Statistical mechanics
- Complex systems
Background
- The Hamiltonian mean-field (HMF) model exhibits long-range interactions and quasistationary states (QSS).
- QSS are traditionally classified by magnetization (M0) and energy (u0), with an out-of-equilibrium phase transition.
- Magnetization fluctuations offer additional insights into QSS dynamics.
Purpose Of The Study
- Characterize the dynamical properties of magnetization fluctuations in the HMF model.
- Investigate the relationship between fluctuation complexity and QSS properties.
- Analyze the role of initial energy (u0) and magnetization (M0) in determining QSS dynamics.
Main Methods
- Utilized permutation entropy (H) and statistical complexity (C) to analyze magnetization fluctuations.
- Compared HMF model dynamics to stochastic processes with power-law spectra (k noise).
- Examined how H and C vary with initial energy (u0) and initial magnetization (M0).
Main Results
- HMF magnetization fluctuations exhibit more structure than purely stochastic processes.
- Global minima in H and C align with the critical energy (u*) separating magnetized and demagnetized QSS.
- Magnetized QSS (low u0) show ordered fluctuations; demagnetized QSS (high u0) exhibit complex, disordered dynamics.
Conclusions
- Permutation entropy and statistical complexity effectively characterize HMF model QSS dynamics.
- Fluctuation complexity is linked to the out-of-equilibrium phase transition in the HMF model.
- The study reveals distinct dynamical signatures for magnetized and demagnetized QSS based on fluctuation complexity.
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