The evolution of quantum irreversible processes can be effectively des
cribed using dynamical semigroups. They involve non-unitary time evolu
tions of density matrices that are generated by completely positive ma
ps. In the case of the neutral kaon system such an approach leads to a
modification of the standard Weisskopf-Wigner evolution, characterize
d by six phenomenological parameters. Bounds on the magnitude of these
parameters could be given using available experimental data. In this
respect, it is remarkable that the condition of complete positivity mi
ght be put to a precise test in future more refined experiments.