与黑洞对偶的尺度不变系统的热机
Heat engines for scale invariant systems dual to black holes
AI总结：
该研究利用 AdS/CFT 对偶，为尺度不变 CFT 热态构造可逆热机，计算多种循环效率并给出 AdS-Schwarzschild 对偶情形下 Stirling 效率的精确结果。
摘要：
根据全息原理，黑洞对偶于强耦合量子系统中的一个热态。全息原理最著名的例子之一是 Anti-de Sitter/Conformal Field Theory（AdS/CFT，反德西特/共形场论）对偶。尽管关于全息热力学已有大量研究，但针对 CFT 热态的热机尚未得到探索。我们构造了可逆热机，其工作物质由 CFT 的静态热平衡态组成。对于对偶于渐近 AdS 黑洞的热态，这实现了 Johnson 的全息热机。我们计算了若干理想化热机的效率，例如 Carnot、Brayton、Otto、Diesel 和 Stirling 循环。大多数热机的效率可以由 CFT 的状态方程导出，而该状态方程源于尺度不变性；我们还将这些效率与理想气体的效率进行了比较。然而，对于一般 CFT，Stirling 效率只有在高温或大体积区间内，才能仅由其特征温度和体积唯一确定。我们推导了对偶于 AdS-Schwarzschild 黑洞的 CFT 态的 Stirling 效率的精确表达式，并将高温区间中的次领先修正与一般 CFT 中的相应修正进行了比较。
英文摘要：
According to holography, a black hole is dual to a thermal state in a strongly coupled quantum system. One of the best-known examples of holography is the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Despite extensive work on holographic thermodynamics, heat engines for CFT thermal states have not been explored. We construct reversible heat engines where the working substance consists of a static thermal equilibrium state of a CFT. For thermal states dual to an asymptotically AdS black hole, this yields a realization of Johnson's holographic heat engines. We compute the efficiency for a number of idealized heat engines, such as the Carnot, Brayton, Otto, Diesel, and Stirling cycles. The efficiency of most heat engines can be derived from the CFT equation of state, which follows from scale invariance, and we compare them to the efficiencies for an ideal gas. However, the Stirling efficiency for a generic CFT is uniquely determined in terms of its characteristic temperature and volume only in the high-temperature or large-volume regime. We derive an exact expression for the Stirling efficiency for CFT states dual to AdS-Schwarzschild black holes and compare the subleading corrections in the high-temperature regime with those in a generic CFT.
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