探索修正的 Kaniadakis 熵：MOND 相关理论、Bekenstein 界猜想与 Landauer 原理下的 Hawking 蒸发
Exploring modified Kaniadakis entropy: MOND-related theory, the Bekenstein bound conjecture, and Hawking evaporation within the Landauer principle
AI总结：
本文利用修正的 Kaniadakis 熵研究黑洞热力学，探讨其在 MOND 理论中的作用，提出该熵精确描述 Bekenstein-Hawking 熵的猜想，验证了 Bekenstein 界在典型 $κ$ 值下成立，并基于 Landauer 原理推导了黑洞蒸发的质量损失表达式。
摘要：
我们研究了利用最近提出的一种修正版 Kaniadakis 熵来描述黑洞热力学。我们讨论了该方案在 Modified Newtonian Dynamics (MOND) 理论中的作用，该理论是牛顿第二定律的推广，旨在不依赖暗物质的情况下解释星系旋转曲线。我们提出一个猜想，即 Kaniadakis 熵精确描述了 Bekenstein-Hawking 黑洞熵。此外，我们考虑了 Bekenstein 界猜想，该猜想对受限量子系统的熵施加了上限。我们在修正的 Kaniadakis 熵背景下分析了该猜想，并发现正如我们的数值研究所证明的那样，它对于典型的 $κ$ 值成立。最后，利用信息论中的 Landauer 原理，我们推导出了黑洞蒸发过程中质量损失的表达式。我们的探索强调了修正的 Kaniadakis 统计学在理解从引力系统到量子力学等多种物理现象中的潜在相关性，为统计力学与物理学中不断增加的其他重要领域之间的交叉研究提供了一个有前景的方向。
英文摘要：
We investigate the description of black-hole thermodynamics in terms of a recently proposed modified version for Kaniadakis entropy. We discuss the role of that proposal within the Modified Newtonian Dynamics (MOND) theory, a generalization of Newton's second law aimed at explaining galaxy rotation curves without resorting to dark matter. We posit a conjecture that the Kaniadakis entropy precisely describes the Bekenstein-Hawking black-hole entropy. Furthermore, we consider the Bekenstein bound conjecture which imposes an upper limit on the entropy of confined quantum systems. We analyze that conjecture in the context of the modified Kaniadakis entropy and find that it holds for typical values of $κ$, as evidenced by our numerical investigation. Finally, using the Landauer principle from information theory, we derive an expression for mass loss in black hole evaporation. Our exploration underscores the potential relevance of a modified Kaniadakis statistics in understanding diverse physical phenomena, from gravitational systems to quantum mechanics, offering a promising direction for future research at the intersection among statistical mechanics and a continually increasing number of other important areas of physics.
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