Volume 83, Number 3, August 2008
|Number of page(s)||6|
|Published online||25 July 2008|
Ergodicity and central-limit theorem in systems with long-range interactions
Instituto de Física, Universidade de Brasília - CP 04455, 70919-970, Brasília, Brazil
Corresponding author: firstname.lastname@example.org
Accepted: 20 June 2008
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.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.20.Dd – Kinetic theory / 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems
© EPLA, 2008
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