  One of the challenges of today's theoretical physics is to fully understand
the connection between a geometrical object like area and a thermostatistical
one like entropy, since area behaves analogously like entropy. The Bekenstein
bound suggests a universal constraint for the entropy of a region in a flat
space. The Bekenstein-Hawking entropy of black holes satisfies the Bekenstein
bound conjecture. In this paper we have shown that when we use important
non-Gaussian entropies, like the ones of Barrow, Tsallis and Kaniadakis in
order to describe the Schwarzschild black hole, then the Bekenstein bound
conjecture seems to fail.
