  We discuss the occurrence of negative specific heat in a nonextensive system
which has an equilibrium second-order phase transition.The specific heat is
negative only in a transient regime before equilibration, in correspondence to
long-lasting metastable states. For these states standard equilibrium
Bolzmann-Gibbs thermodynamics does not apply and the system shows non-Gaussian
velocity distributions, anomalous diffusion and correlation in phase space.
Similar results have recently been found also in several other nonextensive
systems, supporting the general validity of this scenario. These models seem
also to support the conjecture that a nonexstensive statistical formalism, like
the one proposed by Tsallis, should be applied in such cases. The theoretical
scenario is not completely clear yet, but there are already many strong
theoretical indications suggesting that, it can be wrong to consider the
observation of an experimental negative specific heat as an unique and
unambiguous signature of a standard equilibrium first-order phase transition.
