  It is demonstrated that in many thermodynamic textbooks the equivalence of
the different ensembles is achieved in the thermodynamic limit. In this present
work we remark the inequivalence of microcannonical and canonical ensembles in
a finite ultracold system at low energies. We calculate the microcanonical
momentum distribution function (MDF) in a system of identical fermions
(bosons). We find that, the microcanonical MDF deviates from the canonical one,
which is the Fermi-Dirac (Bose-Einstein) function, in a finite system at low
energies where the single-particle density of states and its inverse are
finite.
