First-order microcanonical transitions in finite mean-field modelsM. Antoni1, S. Ruffo2 and A. Torcini3, 2, 1
1 UMR-CNRS 6171 - Université d'Aix-Marseille III Av. Esc. Normandie-Niemen, 13397 Marseille Cedex 20, France
2 Dipartimento d'Energetica "S. Stecco" and CSDC, Università di Firenze, and INFN and INFM - via S. Marta 3, 50139 Firenze, Italy
3 Istituto Nazionale d'Ottica Applicata - Largo E. Fermi 6, 50125 Firenze, Italy
(Received 12 January 2004; accepted in final form 8 April 2004)
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.
05.70.Fh - Phase transitions: general studies.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
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