چکیده
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It has been recently shown that the Bekenstein entropy bound is not respected
by the systems satisfying modified forms of the 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 the Bekenstein entropy, in describing
gravity and related topics indicates different equipartition expressions compared to the usual one.
In that way, the mathematical form of an equipartition theorem can be related to the algebraic
expression of a particular entropy, different from the standard Bekenstein entropy, initially chosen
to describe the black hole event horizon, see Abreu E. M. C. et al., Mod. Phys. Lett. A, 35
(2020) 2050266. 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
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