In this paper, we study the relativistic correction to Bekenstein–Hawking entropy in the canonical ensemble and isothermal–isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann–Gibbs (BG) statistics with its relativistic generalization, Kaniadakis statistics, or \(\kappa \)-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the \(\kappa \rightarrow 0\) limit.

在本文中，我们研究了正则系综和等温等压系综中 Bekenstein-Hawking 熵的相对论修正，并将其应用于非旋转 BTZ 和 AdS-Schwarzschild 黑洞的情况。这是通过概括使用玻尔兹曼-吉布斯 (BG) 统计量及其相对论概括、Kaniadakis 统计量或\(\kappa \)统计量获得的方程来实现的。发现相对论校正本质上是对数的，并且观察到它们的影响在高温限制下变得明显，这表明熵校正必须包括这些相对论校正项，同时采用上述限制。非相对论修正在\(\kappa \rightarrow 0\)极限内恢复。