  Building on the recent solution for the spectrum of the non-commutative well
in two dimensions, the thermodynamics that follows from it is computed. In
particular the focus is put on an ideal fermion gas confined to such a well. At
low densities the thermodynamics is the same as for the commutative gas.
However, at high densities the thermodynamics deviate strongly from the
commutative gas due to the implied excluded area resulting from the
non-commutativity. In particular there are extremal macroscopic states,
characterized by area, number of particles and angular momentum, that
correspond to a single microscopic state and thus have vanishing entropy. When
the system size and excluded area are comparable, thermodynamic quantities,
such as entropy, exhibit non-extensive features.
