A holographic proof of Rényi entropic inequalities
A holographic proof of Rényi entropic inequalities
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DOI：
10.1007/jhep12(2016)129
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发表时间：
2016-12
影响因子：
5.4
通讯作者：
Yūki Nakaguchi;T. Nishioka
中科院分区：
文献类型：
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作者：
Yūki Nakaguchi;T. Nishioka
我们证明了Rényi熵不等式在全息设置的基础上最近提出的全息公式的Rényi熵的体积是稳定的任何扰动。把Rényi参数看作温度的倒数，用统计力学的方法重新表述了熵，从而把不等式简洁地解释为熵、能量和热容的正性.这个类比也使推导全息公式的热力学结构变得清晰。作为证明的副产品，我们得到了一个全息公式来计算量子涨落的模哈密顿量。纠缠的能力的几个例子进行了详细研究。
We prove Rényi entropic inequalities in a holographic setup based on the recent proposal for the holographic formula of Rényi entropies when the bulk is stable against any perturbation. Regarding the Rényi parameter as an inverse temperature, we reformulate the entropies in analogy with statistical mechanics, which provides us a concise interpretation of the inequalities as the positivities of entropy, energy and heat capacity. This analogy also makes clear a thermodynamic structure in deriving the holographic formula. As a by-product of the proof we obtain a holographic formula to calculate the quantum fluctuation of the modular Hamiltonian. A few examples of the capacity of entanglement are examined in detail.