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Nonergodicity and central-limit behavior for long-range Hamiltonians

2007/06/30 by A. Pluchino, A. Rapisarda, C. Tsallis · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Attractor #Chaotic #Equidistant #Ergodicity #Hamiltonian (control theory) #Limit (mathematics) #Metastability #Quantum chaos and dynamical systems #Quantum many-body systems #astro-ph #cond-mat.stat-mech #nucl-th #physics.data-an

paper · pdf · doi:10.1209/0295-5075/80/26002

published as Europhysics Letters, 80 (2007) 26002 · 6 pages 7 figures. Improved version accepted for publication on Europhysics Letters

arxiv created 2007/09/03 · openalex publication_date 2007/09/21 · arxiv updated 2011/11/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We present a molecular dynamics test of the Central-Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime (specifically, at thermal equilibrium), ergodicity is essentially verified, and the Pdfs of the sums appear to be Gaussians, consistently with the standard CLT. When the system is, instead, only weakly chaotic (specifically, along longstanding metastable Quasi-Stationary States), nonergodicity ( i.e. , discrepant ensemble and time averages) is observed, and robust q -Gaussian attractors emerge, consistently with recently proved generalizations of the CLT.

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