AI 中文总结
该研究将满足热力学第三定律的信息论黑洞熵扩展至引力及克尔-纽曼情形，通过微扰方法证明其可由广义相对论红外形变重现，还区分了几何极端性与统计冻结终点。
AI 中文摘要
我们研究满足热力学第三定律能斯特表述的信息论黑洞熵的引力及克尔-纽曼（Kerr-Newman）扩展。该熵被定义为依赖质量的伯努利系综与无偏参考系综之间的Kullback-Leibler散度，因此衡量的是相对信息而非黑洞微观态数的对数。我们通过微扰方法证明，其温度和熵可通过广义相对论的红外形变重现。在形变耦合的线性阶，表面引力温度与Wald熵均与信息论结果一致。在一个具体实现中，这种匹配产生了正的有效宇宙学项，其微小性与大的微观参数N相关。我们还基于不可约质量提出了克尔-纽曼黑洞的扩展方案，该构造保留了与视界面积及半经典极限的联系，同时区分了几何极端性与普适的统计冻结终点，该终点与角动量和电荷无关。
英文摘要
We investigate gravitational and Kerr-Newman extensions of an information-theoretic black-hole entropy that satisfies the Nernst formulation of the third law of thermodynamics. The entropy is identified with the Kullback-Leibler divergence between a mass-dependent Bernoulli ensemble and an unbiased reference ensemble, and therefore measures relative information rather than the logarithm of the number of black-hole microstates. We show perturbatively that its temperature and entropy can be reproduced by an infrared deformation of General Relativity. To linear order in the deformation couplings, the surface-gravity temperature and the Wald entropy agree with the information-theoretic results. In an explicit realization, the matching generates a positive effective cosmological term whose smallness is related to the large microscopic parameter $N$. We also propose an extension to Kerr-Newman black holes based on the irreducible mass. This construction preserves the connection with the horizon area and the semiclassical limit, while distinguishing geometrical extremality from the universal statistical-freezing endpoint, which is independent of angular momentum and charge.
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