  A microcanonical first order transition, connecting a clustered to a
homogeneous phase, is studied from both the thermodynamic and dynamical point
of view for a N-body Hamiltonian system with infinite-range couplings. In the
microcanonical ensemble specific heat can be negative, but besides that, a
microcanonical first order transition displays a temperature discontinuity as
the energy is varied continuously (a dual phenomenon to the latent heat in the
canonical ensemble). In the transition region, the entropy per particle
exhibits, as a function of the order parameter, two relative maxima separated
by a minimum. The relaxation of the metastable state is shown to be ruled by an
activation process induced by intrinsic finite N fluctuations. In particular,
numerical evidences are given that the escape time diverges exponentially with
N, with a growth rate given by the entropy barrier.
