First-order microcanonical transitions in finite mean-field models

A microcanonical first-order transition, connecting a clustered to a homogeneous phase, is studied from both the thermodynamic and the dynamical point of view for an 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.