  In this work, we evaluate the Shannon-like entropic measure of
spatially-localized functions for a five-dimensional braneworld generated by a
double sine-Gordon (DSG) potential. The differential configurational entropy
(DCE) has been shown in several recent works to be a configurational
informational measure (CIM) that selects critical points and brings out phase
transitions in confined energy models with arbitrary parameters. We select the
DSG scenario because it presents an energy-degenerate spatially localized
profile where the solutions to the scalar field demonstrate critical behavior
that is only a result of geometrical effects. As we will show, the DCE
evaluation provides a method for predicting the existence of a transition
between the phases of the domain wall solutions. Moreover, the entropic measure
reveals information about the model that is capable of describing the phase
sector where we obtain resonance modes on the massive spectra of the graviton.
The graviton resonance lifetimes are related to the existence of scales on
which 4D gravity is recovered. Thus, we correlate the critical points defined
by the {CIMs} with the existence of resonances and their lifetimes. To extend
our research regarding this system, we calculate the corrections to Newton's
Law coming from the graviton modes.
