Description
We review the Bekenstein bound for thermodynamic entropy, and its dervation from arguments of black hole physics. Then we consider different generalized entropies as Tsallis-Cirto, Barrow, Tsallis-Jensen, and Renyi entropies. Thus, we establish new quantitative bounds on such entropies, arriving in this way to new formulations of the Bekenstein bound itself. We also briefly comment on the connections between the Bekenstein bound and the (generalized) uncertainty principle.