It was shown recently that extended black hole thermodynamics, where the cosmological constant is a dynamical variable, giving rise to a pressure 𝑝 and its conjugate volume 𝑉, can be given a natural setting in the context of braneworld models. We study the specific heat capacities 𝐶𝑝⁡(𝑇) and 𝐶𝑉⁡(𝑇) of the quantum version of the Bañados, Teitelboim, and Zanelli (BTZ) black hole that lives in the induced gravity theory on the brane. There are multiple branches of solutions, and we explore and characterize key features of the possible behavior. We identify and study a critical point in the space of solutions where both specific heats diverge. In the regime of weak backreaction where we are close to an ordinary theory of gravity, the black hole is “subentropic,” but as backreaction is increased we note that there are parts of parameter space that has regions where it is “superentropic.” While a study of the sign of the specific heats does not always show a corresponding instability (conjectured in the literature), the presence of strong backreaction makes interpretation unclear.

中文翻译：

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扩展热力学中量子 BTZ 黑洞的比热


最近研究表明，在布朗世界模型的背景下，可以赋予扩展黑洞热力学，其中宇宙学常数是一个动态变量，产生压力 p 及其共轭体积 V。我们研究了 Bañados、Teitelboim 和 Zanelli （BTZ） 黑洞的量子版本的比热容 Cp（T） 和 CV（T），该黑洞存在于 bran上的诱导引力理论中。解决方案有多个分支，我们探索和描述可能行为的关键特征。我们确定并研究解决方案空间中两种比热发散的关键点。在我们接近普通引力理论的弱反反应状态中，黑洞是“亚熵”的，但随着反反应的增加，我们注意到参数空间的某些部分具有“超熵”的区域。虽然对比热符号的研究并不总是显示相应的不稳定性（在文献中猜想），但强烈的反反应的存在使解释不清楚。