  A Hamiltonian model living in a bounded phase space and with long-range
interactions is studied. It is shown, by analytical computations, that there
exists an energy interval in which the microcanonical entropy is a decreasing
convex function of the total energy, meaning that ensemble equivalence is
violated in a negative-temperature regime. The equilibrium properties of the
model are then investigated by molecular dynamics simulations: first, the
caloric curve is reconstructed for the microcanonical ensemble and compared to
the analytical prediction, and a generalized Maxwell-Boltzmann distribution for
the momenta is observed; then, the nonequivalence between the microcanonical
and canonical descriptions is explicitly shown. Moreover, the validity of
Fluctuation-Dissipation Theorem is verified through a numerical study, also at
negative temperature and in the region where the two ensembles are
nonequivalent.
