  A simple, exactly solvable statistical model is presented for the description
of baryonic matter in the thermodynamic conditions associated to the evolution
of core-collapsing supernova. It is shown that the model presents a first order
phase transition in the grandcanonical ensemble which is not observed in the
canonical ensemble. Similar to other model systems studied in condensed matter
physics, this ensemble in-equivalence is accompanied by negative susceptibility
and discontinuities in the intensive observables conjugated to the order
parameter. This peculiar behavior originates from the fact that baryonic matter
is subject to attractive short range strong forces as well as repulsive long
range electromagnetic interactions, partially screened by a background of
electrons. As such, it is expected in any theoretical treatment of nuclear
matter in the stellar environment. Consequences for the phenomenology of
supernova dynamics are drawn.
