Maximal Shannon entropy in the vicinity of an exceptional point in an open microcavity

The Shannon entropy as a measure of information contents is investigated around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system. The Shannon entropy is maximized near the EP in the parameter space for two interacting modes, but the exact maximum position is slightly off the EP toward the weak interaction region while the slopes of the Shannon entropies diverge at the EP. The Shannon entropies also show discontinuity across a specific line in the parameter space, directly related to the exchange of the Shannon entropy as well as the mode patterns with that line as a boundary. This feature results in a nontrivial topological structure of the Shannon entropy surfaces.