Gabriele Martelloni — SISSA Trieste #
Generalized maximum entropy approach to explain quasi-stationary states in long range systems #
Systems with long-range interactions display a short-time relaxation towards quasistationary states (QSS) 
whose lifetime increases with the system size. In the paradigmatic Hamiltonian mean-field model (HMF) 
out-of-equilibrium phase transitions are predicted and numerically detected which separate homogeneous 
(zero magnetization) and inhomogeneous (nonzero magnetization) QSS. In the former regime, the velocity 
distribution presents two large, symmetric, bumps, which cannot be self-consistently explained by 
resorting to the conventional Lynden-Bell maximum entropy approach. To improve the theory in this respect 
and eventually fill the gap with the observation, we here propose a generalized maximum entropy scheme 
which accounts for the pseudo-conservation of a additional charges, the even momenta of the single 
particle distribution.  These latter are set to the asymptotic values, as estimated by direct integration 
of the underlying Vlasov equation, which formally holds in the thermodynamic limit. Methodologically, we 
operate in the framework of generalized Gibbs ensemble, as sometimes defined in statistical quantum 
mechanics, which contains an infinite number of conserved charges. The agreement between theory and 
simulations is extremely satisfying, both above and below the out of equilibrium transition threshold. The 
fine details of the velocity profile are adequately captured upon truncation at the tenth order in the 
hierarchy of pseudo-conserved momenta.