  The puzzling properties of the first order phase transition in YbInCu$_4$ and
its alloys in the wide range of magnetic fields and temperatures are perfectly
described in terms of a simple entropy transition for free Yb ions. In
particular, it turns out that the transition line in the $(B,T)$-plane is very
close to the elliptic shape, as it has been observed experimentally. Similar
calculations are done, and the experiments are proposed for the
$(\gamma{-}\alpha)$ phase transition in Ce in Megagauss fields. We speculate,
that in case of YbInCu$_4$ the first order transition is a Mott transition
between a higher temperature phase in which localized moments are stabilized by
the entropy terms in the free energy, and a band-like non-magnetic ground state
of the $f$-electrons.
