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.

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