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

S. Chandran, S. Shankaranarayanan
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引用次数: 2

Abstract

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.
纠缠力学与黑洞热力学的一对一对应关系
我们分别建立了纠缠熵、能量和温度(量子纠缠力学)与黑洞熵、科玛能量和霍金温度之间的一对一映射关系。对于具有单视界和多视界的四维球对称渐近平坦和非平坦时空,我们明确地证明了这一点。我们利用了纠缠熵固有的尺度对称,并确定了产生无限多个具有相同纠缠熵的系统的尺度变换,这些系统仅通过各自的能量和温度来区分。我们证明了这种尺度对称性存在于大多数已知的系统中,从球对称时空中的双耦合谐振子到量子标量场。尺度对称性使我们能够确定纠缠熵发散到系统中(近)零模产生的原因。我们使用合适的边界条件系统地分离了零模贡献。我们证明了量子标量场的纠缠熵和能量在具有视界和平坦时空的时空中具有不同的尺度。与视界的热力学结构类似,E=2TS关系在纠缠图象中也被普遍满足。然后,我们证明了在渐近平坦和非平坦时空下,黑洞热力学的smarr -公式存在一一对应关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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