  We introduce Shannon's information entropy to characterize the avoided
crossing appearing in the resonant Zener-like phenomenon in ultrasonic
superlattices made of two different fluidlike meta- materials. We show that
Shannon's entropy gives a correct physical insight of the localization effects
taking place and manifest the informational exchange of the involved acoustic
states in the narrow region of parameters where the avoided crossing occurs.
Results for ultrasonic structures consisting of alternating layers of
methyl-metacrylate and water cavities, in which the acoustic Zener effect were
recently demonstrated, are also reported.
