  For quantum mechanical systems an entropy-like quantity $S_q$ is defined.
$S_q$ can differ from the usually defined entropy $S$ and $S_q$ may increase
with time for an isolated system. The essential condition for the difference
between $S$ and $S_q$ is the assumption that the set {\bf A} of observables
which can be represented by a measurement is a proper subset of the set of
selfadjoint operators. The underlying idea is made visible in the case of
particle systems with non-trivial scattering. The model-character of the
reasoning comes from the fact that continuous spectra are replaced by
point-spectra. So it seems evident, that no direct connection exists between
$S_q$ and the Sinai-Kolmogorov-Entropy at least in this model with pure
point-spectra.
