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Abstract: We present a molecular dynamics test of the Central Limit Theorem CLT in aparadigmatic long-range-interacting many-body classical Hamiltonian system, theHMF model. We calculate sums of velocities at equidistant times alongdeterministic trajectories for different sizes and energy densities. We showthat, when the system is in a chaotic regime specifically, at thermalequilibrium, ergodicity is essentially verified, and the Pdfs of the sumsappear to be Gaussians, consistently with the standard CLT. When the system is,instead, only weakly chaotic specifically, along longstanding metastableQuasi-Stationary States, nonergodicity i.e., discrepant ensemble and timeaverages is observed, and robust $q$-Gaussian attractors emerge, consistentlywith recently proved generalizations of the CLT.



Autor: A. Pluchino, A. Rapisarda, C. Tsallis

Fuente: https://arxiv.org/







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