Volume 80, Number 2, October 2007
Article Number 26002
Number of page(s) 6
Section Condensed Matter: Structural, Mechanical and Thermal Properties
Published online 21 September 2007
EPL, 80 (2007) 26002
DOI: 10.1209/0295-5075/80/26002

Nonergodicity and central-limit behavior for long-range Hamiltonians

A. Pluchino1, A. Rapisarda1 and C. Tsallis2, 3

1  Dipartimento di Fisica e Astronomia, Università di Catania, and INFN sezione di Catania - Via S. Sofia 64, I-95123 Catania, Italy
2  Centro Brasileiro de Pesquisas Fisicas - Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
3  Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, NM 87501, USA

received 27 June 2007; accepted in final form 1 September 2007; published October 2007
published online 21 September 2007

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.

64.60.My - Metastable phases.
89.75.-k - Complex systems.

© Europhysics Letters Association 2007