  It was recently shown that, in general, the von Neumann spin entropy of
fermionic particles is not invariant under Lorentz boosts. We show that an
analogous result can be recovered (at the lowest order of $v^2 /c^2$) using
plain nonrelativistic quantum mechanics provided one uses that energy weighs:
$E=m c^2$. This should (i) help to moderate the skepticism on the
observer-dependence of the spin entropy of fermionic particles, (ii) emphasize
the soft relativistic nature of this result, and (iii) show that this is a
particular case of a more general class of systems, since our calculation only
assumes a nonrelativistic particle endowed with an internal degree of freedom.
