  The phenomenon of partial equivalence of statistical ensembles is illustrated
by discussing two examples, the mean-field XY and the mean-field spherical
model. The configurational parts of these systems exhibit partial equivalence
of the microcanonical and the canonical ensemble. Furthermore, the
configurational microcanonical entropy is a smooth function, whereas a
nonanalytic point of the configurational free energy indicates the presence of
a phase transition in the canonical ensemble. In the presence of a standard
kinetic energy contribution, partial equivalence is removed and a
nonanalyticity arises also microcanonically. Hence in contrast to the common
belief, kinetic energy, even though a quadratic form in the momenta, has a
non-trivial effect on the thermodynamic behaviour. As a by-product we present
the microcanonical solution of the mean-field spherical model with kinetic
energy for finite and infinite system sizes.
