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A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model

Andrea Antoniazzi·Duccio Fanelli·Julien Barré·Pierre-Henri Chavanis·Thierry Dauxois·Stefano Ruffo
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Abstract

A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that a maximum entropy principle applied to the associated Vlasov equation explains known features of such states for a wide range of initial conditions. We are able to reproduce velocity distribution functions with an analytical expression which is derived from the theory with no adjustable parameters. A normal diffusion of angles is detected and a new dynamical effect, two oscillating clusters surrounded by a halo, is also found and theoretically justified.

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Andrea Antoniazzi, Duccio Fanelli, Julien Barré, Pierre-Henri Chavanis, Thierry Dauxois, Stefano Ruffo. 2006-08-16. A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model. https://doi.org/10.1103/physreve.75.011112

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