Ergodicity and central-limit theorem in systems with long-range interactions

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Published 25 July 2008 Europhysics Letters Association
, , Citation A. Figueiredo et al 2008 EPL 83 30011 DOI 10.1209/0295-5075/83/30011

0295-5075/83/3/30011

Abstract

In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian mean-field model and show that the lifetime of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central-limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.

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10.1209/0295-5075/83/30011