Statistical theory of quasi stationary states beyond the single   water-bag case study
  An analytical solution for the out-of-equilibrium quasi-stationary states of the paradigmatic Hamiltonian Mean Field (HMF) model can be obtained from a maximum entropy principle. The theory has been so far tested with reference to a specific class of initial condition, the so called (single-level) water-bag type. In this paper a step forward is taken by considering an arbitrary number of overlapping water bags. The theory is benchmarked to direct microcanonical simulations performed for the case of a two-levels water-bag. The comparison is shown to return an excellent agreement. 
Mallbor Assllani, Duccio Fanelli, Alessio Turchi, Timoteo Carletti,   Xavier Leoncini
cond-mat.stat-mech