  Information entropies associated with the energy density in position and
momentum spaces are build for an anti-de Sitter (AdS) black hole. These
quantities, that satisfy an entropic uncertainty relation, vary with the
temperature. The higher is the black hole temperature, the greater/smaller is
the information encoded respectively in the position/momentum distributions of
energy. On the other hand, as it is well know, AdS black holes are subject to
the Hawking Page phase transition. The amplitude for dominance of the black
hole phase over the thermal AdS phase increases with the temperature. So, as
the system becomes more stable, there is a change in the way that information
is stored. In particular: information stored in the spatial energy density
increases while information stored in the energy density in momentum space
decreases.
