  In contrast to the canonical case, microcanonical thermodynamic functions can
show nonanalyticities also for finite systems. In this paper we contribute to
the understanding of these nonanalyticities by working out the relation between
nonanalyticities of the microcanonical entropy and its configurational
counterpart. If the configurational microcanonical entropy $\omega_N^c(v)$ has
a nonanalyticity at $v=v_c$, then the microcanonical entropy
$\omega_N(\epsilon)$ has a nonanalyticity at the same value $\epsilon=v_c$ of
its argument for any finite value of the number of degrees of freedom $N$. The
presence of the kinetic energy weakens the nonanalyticities such that, if the
configurational entropy is $p$ times differentiable, the entropy is $p+\lfloor
N/2 \rfloor$-times differentiable. In the thermodynamic limit, however, the
behaviour is very different: The nonanalyticities do not longer occur at the
same values of the arguments, but the nonanalyticity of the microcanonical
entropy is shifted to a larger energy. These results give a general explanation
of the peculiar behaviour previously observed for the mean-field spherical
model. With the hypercubic model we provide a further example illustrating our
results.
