Tsallis uncertainty.

It has already been shown that the Bekenstein entropy bound is not respected by the systems satisfying modified forms of Heisenberg uncertainty principle (HUP) including the generalized and extended uncertainty principles, or even their combinations. On the other hand, the use of generalized entropies, which differ from Bekenstein entropy, in describing gravity and related topics guides us to different equipartition expressions compared to the usual one, and indeed, the validity of Bekenstein entropy, HUP, and usual equipartition theorem is tied together (arXiv:2002.02435). Motivated by these works, we address three new uncertainty principles leading to recently introduced generalized entropies. In addition, the corresponding energy-time uncertainty relations and Unruh temperatures are also calculated. As a result, it seems that systems described by generalized entropies, such as those of Tsallis, do not necessarily meet HUP and may satisfy modified forms of HUP.