标题： 纠缠熵能否是黑洞熵的来源？ 显示英文标题

标题： Can the entanglement entropy be the origin of black-hole entropy ?

摘要： 纠缠熵常被认为是黑洞熵的起源的有力候选。 为了判断这种推测是否正确，有效的方法是研究从纠缠熵获得的整体热力学结构，而不是仅仅检查熵的表观结构或将其与黑洞熵进行比较。 这是因为当熵与系统的能量和温度相关时，它才具有物理意义。 从这个观点出发，我们通过引入纠缠能来构建“纠缠热力学”，并与黑洞热力学进行比较。 我们考虑了纠缠能的两种可能定义。 然后我们通过将这些不同的纠缠能定义与纠缠熵结合，构建了两种不同类型的热力学。 我们发现，如果不考虑引力效应，这两种热力学都与黑洞热力学有显著差异。 这些差异在热力学第三定律的背景下尤为明显。 最后，我们看到引力的包含如何改变纠缠热力学。 我们给出一个有说服力的论点，即如果适当包含引力效应，纠缠热力学的行为会像黑洞热力学一样。 因此，纠缠熵通过了一个非平凡的检验，以确认其作为黑洞熵的起源。 显示英文摘要

摘要： Entanglement entropy is often speculated as a strong candidate for the origin of the black-hole entropy. To judge whether this speculation is true or not, it is effective to investigate the whole structure of thermodynamics obtained from the entanglement entropy, rather than just to examine the apparent structure of the entropy alone or to compare it with that of the black hole entropy. It is because entropy acquires a physical significance only when it is related to the energy and the temperature of a system. From this point of view, we construct a `thermodynamics of entanglement' by introducing an entanglement energy and compare it with the black-hole thermodynamics. We consider two possible definitions of entanglement energy. Then we construct two different kinds of thermodynamics by combining each of these different definitions of entanglement energy with the entanglement entropy. We find that both of these two kinds of thermodynamics show significant differences from the black-hole thermodynamics if no gravitational effects are taken into account. These differences are in particular highlighted in the context of the third law of thermodynamics. Finally we see how inclusion of gravity alter the thermodynamics of the entanglement. We give a suggestive argument that the thermodynamics of the entanglement behaves like the black-hole thermodynamics if the gravitational effects are included properly. Thus the entanglement entropy passes a non-trivial check to be the origin of the black-hole entropy.