Maximum entropy principle explains quasistationary states in systems with long-range interactions: the example of the Hamiltonian mean-field model.
A generic feature of systems with long-range interactions is the presence of quasistationary states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian mean-field 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 analytic expression which is derived from the theory with no adjustable parameters. A normal diffusion of angles is detected, which is consistent with Gaussian tails of velocity distributions. A dynamical effect, two oscillating clusters surrounded by a halo, is also found and theoretically justified.
Antoniazzi
Andrea
A
Dipartimento di Energetica and CSDC, Università di Firenze, and INFN, via S. Marta, 3, 50139 Firenze, Italy.
Fanelli
Duccio
D
Barré
Julien
J
Chavanis
Pierre-Henri
PH
Dauxois
Thierry
T
Ruffo
Stefano
S