The Bekenstein bound, inspired by the physics of black holes, is introduced to constrain the entropy growth of a physical system down to the quantum level in the context of a generalized second law of thermodynamics. We first show that the standard Bekenstein bound is violated when the entropy of a Schwarzschild black hole is described in non-Gaussian statistics Barrow, Tsallis, and Kaniadakis due to the presence of the related indices Δ, q and κ, respectively. Then, by adding the GUP effects into the Bekenstein bound, we find that the generalized bound is satisfied in the context of the mentioned entropies through a possible connection between the entropies indices and the GUP parameter β.

中文翻译：

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非高斯统计中黑洞熵的贝肯斯坦束缚


受黑洞物理学的启发，引入贝肯斯坦边界是为了在广义热力学第二定律的背景下将物理系统的熵增长限制到量子水平。我们首先表明，当在非高斯统计 Barrow、Tsallis 和 Kaniadakis 中描述施瓦西黑洞的熵时，由于分别存在相关指数 Δ、q 和 κ，违反了标准的贝肯斯坦边界。然后，通过将 GUP 效应添加到 Bekenstein 边界中，我们发现通过熵指数和 GUP 参数β之间的可能联系，在上述熵的上下文中满足广义边界。