  The physical meaning of entropy is analyzed in the context of statistical,
nuclear, atomic physics and cosmology. Only the microcanonical Boltzmann
entropy leads to no contradictions in several simple, elementary and for
thermodynamics important situations. The conventional canonical statistics
implies several serious errors and misinterpretations. This has far reaching
consequences for phase-separations as well for the usual formulations of the
second law. Applications in cosmology suffer under the ubiquitous use of
canonical statistics. New reformulations in terms of microcanonical statistics
are highly demanded but certainly difficult.
