  In the framework of a 2D Vlasov model, we study the time evolution of the
"coarse-grained" Generalized Entropy (GE) in a nuclear system which undergoes a
multifragmentation (MF) phase transition. We investigate the GE both for the
gas and the fragments (surface and bulk part respectively). We find that the
formation of the surface causes the growth of the GE during the process of
fragmentation. This quantity then characterizes the MF and confirms the crucial
role of deterministic chaos in filling the new available phase-space: at
variance with the exact time evolution, no entropy change is found when the
linear response is applied. Numerical simulations were used also to extract
information about final temperatures of the fragments. From a fitting of the
momentum distribution with a Fermi-Dirac function we extract the temperature of
the fragments at the end of the process. We calculate also the gas temperature
by averaging over the available phase space. The latter is a few times larger
than the former, indicating a gas not in equilibrium. Though the model is very
schematic, this fact seems to be very general and could explain the discrepancy
found in experimental data when using the slope of light particles spectra
instead of the double ratio of isotope yields method in order to extract the
nuclear caloric curve.
