  The relation between the Shannon entropy and avoided crossings is
investigated in dielectric microcavities. The Shannon entropy of probability
density for eigenfunctions in an open elliptic billiard as well as a closed
quadrupole billiard increases as the center of avoided crossing is approached.
These results are opposite to those of atomic physics for electrons. It is
found that the collective Lamb shift of the open quantum system and the
symmetry breaking in the closed chaotic quantum system give equivalent effects
to the Shannon entropy.
