2008/05/12 by Annibal Figueiredo, Ana Elisa Bastos Figueiredo, T. M. Rocha Filho +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Attractor #Central limit theorem #Complex Systems and Time Series Analysis #Computer science #Ergodicity #Gaussian #Limit (mathematics) #Mathematical analysis #Mathematics #Particle system #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Statistics #Weak convergence #cond-mat.stat-mech
paper · pdf · doi:10.1209/0295-5075/83/30011
13 pages,6 figures
arxiv created 2008/05/12 · openalex publication_date 2008/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.