In a profound way, entropy represents a concept and a measure of uncertainty. It has been shown that the uncertainty in Quantum Mechanics namely the Heisenberg principle, is a consequence of the entropic uncertainty principle. Additionally in several theoretical frameworks, the Heisenberg uncertainty principle needs to be extended to a Generalized Uncertainty Principle (GUP) to describe the quantum effects of gravity. GUP emerges from considerations in superstring theory, and also from a Gedankenexperiment of black-hole diffraction. Then, given that Heisenberg's uncertainty principle arises from the uncertainty in entropy, it is therefore natural to ask whether GUP can also be deduced from the entropic uncertainty when generalized entropies are considered. We work with generalized entropies presented in previous works, that depend only on the probability, $S_{\pm}$. We show that GUP is a consequence of the entropic principle associated with these statistics. Also, we analyze the corrections to the energy levels for the simple harmonic oscillator with this method (entropic GUP), where, those are the same as the ones found in the usual GUP literature. Different statistics lead to distinct commutation relations for the canonical variables. However, the corrections to the usual commutators show a universality with respect to the entropy measure, with corrections of the order of the Planck scale.

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作为广义不确定性原理起源的修正熵

在深刻的意义上，熵代表了一个概念和不确定性的度量。已经表明，量子力学中的不确定性，即海森堡原理，是熵不确定性原理的结果。此外，在几个理论框架中，海森堡不确定性原理需要扩展到广义不确定性原理 (GUP) 来描述引力的量子效应。GUP 源于超弦理论的考虑，也源于黑洞衍射的格丹肯实验。然后，鉴于海森堡的不确定性原理源于熵的不确定性，因此很自然地要问，当考虑广义熵时，是否也可以从熵的不确定性推导出 GUP。我们使用以前作品中提出的广义熵，仅取决于概率 $S_{\pm}$。我们表明 GUP 是与这些统计数据相关的熵原理的结果。此外，我们使用这种方法（熵 GUP）分析了对简谐振子能级的修正，其中，这些修正与通常 GUP 文献中的修正相同。不同的统计数据导致典型变量的不同对易关系。然而，对普通交换子的修正显示了熵测度的普遍性，修正了普朗克尺度的阶数。这些与通常的 GUP 文献中的相同。不同的统计数据导致典型变量的不同对易关系。然而，对普通交换子的修正显示了熵测度的普遍性，修正了普朗克尺度的阶数。这些与通常的 GUP 文献中的相同。不同的统计数据导致典型变量的不同对易关系。然而，对普通交换子的修正显示了熵测度的普遍性，修正了普朗克尺度的阶数。