AI 中文总结
构建四维反德西特黑洞视界微观结构描述，通过组合学直接得熵，有限填充下主导项与面积成正比，再现霍金定律。次主导修正含对数项和逆面积展开，还从扩展定律获热力学依据，组合学提供主导熵，热力学扇区确定平衡填充等。
AI 中文摘要
在这项工作中，我们构建了四维反德西特黑洞的视界微观结构描述，其中面积为\(A\)的视界被分解为\(\mathcal{N}=A/a_p\)个微观位点和\(N\)个被占据的视界位点。核心结果是，这种部分占据的视界扇区的组合学直接产生熵：在有限填充 regime 中，主导项与面积成正比，最大熵填充再现了贝肯斯坦 - 霍金定律，\(a_p = 4\ln2\ \ell_{p}^{2}\)。次主导修正包括一个减法对数项和一个逆面积展开。然后我们表明，这种部分占据 regime 从具有化学势\(\mu\)、与斯马尔一致的激发焓\(\delta M(A,P,N)\)和反德西特控制参数\(u = PS\)的扩展第一定律中获得热力学依据。在这种解释中，组合学提供了主导的视界熵，而热力学扇区提供了一种修饰，用于选择平衡填充并为偏离参考部分占据配置分配有限的激发成本。
英文摘要
In this work we formulate a horizon-microstructure description of four-dimensional AdS black holes in which a horizon of area $A$ is resolved into $\mathcal{N}=A/a_p$ microscopic sites and $N$ occupied horizon sites. The central result is that the combinatorics of this partially occupied horizon sector yields the entropy directly: in the finite-filling regime the leading term is proportional to the area, and the maximal-entropy filling reproduces the Bekenstein--Hawking law with $a_p=4\ln 2\ \ell_{p}^{2}$. Subleading corrections include a subtractive logarithmic term and an inverse-area expansion. We then show that this partially occupied regime admits a thermodynamic justification from an extended first law with chemical potential $μ$, a Smarr-consistent excitation enthalpy $δM(A,P,N)$, and an AdS control parameter $u=PS$. In this interpretation, the combinatorics provides the dominant horizon entropy, while the thermodynamic sector supplies a dressing that selects the equilibrium filling and assigns a finite excitation cost to departures from a reference partially occupied configuration.
