论文标题

纠缠力学与黑洞热力学之间的一对S对应关系

One-to-one correspondence between entanglement mechanics and black hole thermodynamics

论文作者

Chandran, S. Mahesh, Shankaranarayanan, S.

论文摘要

我们分别在黑洞熵,科马尔能量和鹰温度的温度下,在纠缠熵,能量和温度(量子纠缠力学)之间建立了一对一的映射。我们明确地显示了具有单个和多个范围的4-D球形对称渐近和非平板空间时间。我们利用纠缠熵的固有缩放对称性,并确定缩放变换,该变换产生了具有相同纠缠熵的无限系统,仅由它们各自的能量和温度区别。我们表明,从两耦合的谐波振荡器到球形对称时空中的量子标量字段开始,大多数知名的系统中存在这种缩放对称性。缩放对称性使我们能够确定系统中(接近)零模型生成(接近)零模型的纠缠熵的原因。我们使用合适的边界条件系统地隔离零模式贡献。我们表明,在水平和平坦时空的空间时间里,量子标量场尺度的纠缠熵和能量不同。关系$ e = 2TS $类似于地平线的热力学结构,在纠缠图中也普遍满足。然后,我们证明存在一对一的对应关系,导致黑洞热力学的Smarr形式用于渐近平坦和非平板空间时间。

We establish a one-to-one mapping between entanglement entropy, energy, and temperature (quantum entanglement mechanics) with black hole entropy, Komar energy, and Hawking temperature, respectively. We show this explicitly for 4-D spherically symmetric asymptotically flat and non-flat space-times with single and multiple horizons. We exploit an inherent scaling symmetry of entanglement entropy and identify scaling transformations that generate an infinite number of systems with the same entanglement entropy, distinguished only by their respective energies and temperatures. We show that this scaling symmetry is present in most well-known systems starting from the two-coupled harmonic oscillator to quantum scalar fields in spherically symmetric space-time. The scaling symmetry allows us to identify the cause of divergence of entanglement entropy to the generation of (near) zero-modes in the systems. We systematically isolate the zero-mode contributions using suitable boundary conditions. We show that the entanglement entropy and energy of quantum scalar field scale differently in space-times with horizons and flat space-time. The relation $E=2TS$, in analogy with the horizon's thermodynamic structure, is also found to be universally satisfied in the entanglement picture. We then show that there exists a one-to-one correspondence leading to the Smarr-formula of black hole thermodynamics for asymptotically flat and non-flat space-times.

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