  In the holographic AdS/QCD approach, the confinement/deconfinement transition
is associated with the Hawking-Page transition of a thermal anti-de Sitter
(AdS) space to an AdS black hole. In the case of the hard wall model, the
thermal transition takes place in the planar AdS thanks to the introduction of
an infrared cut-off in the geometry. The corresponding thermodynamic entropy of
the $SU(N) $ gauge theory jumps from proportional to $N^0$ in the confined
hadronic phase to proportional to $N^2$ in the plasma phase, corresponding to
the presence of the color degrees of freedom. The Hawking-Page transition is
understood by considering a semiclassical picture of a system consisting of two
different geometries that are asymptotically AdS. One is the AdS black hole and
the other the thermal AdS space. The relative stability between these competing
geometries varies with the temperature. So, the transition is essentially a
problem of stability. An interesting tool to study stability of physical
systems is the configuration entropy (CE), inspired in the Shannon
informational entropy. In this work we investigate the CE for the case of the
AdS/QCD hard wall model at finite temperature. We propose a regularized form
for the energy densities of the black hole (BH) and of the thermal AdS
geometries that makes it possible to calculate their CEs as a function of the
temperature. We find a relation between stability and the value of the CE for
the system of asymptotically AdS geometries. Remarkably, it is found that the
CE is proportional to $\log(T)$, where $T$ is the temperature. This result
makes it possible to write out a simple relation between the configuration and
the thermodynamic entropies.
