We study the entanglement entropy and the mutual information in coupled harmonic systems at finite temperature. Interestingly, we find that the mutual information does not vanish at infinite temperature, but it rather reaches a specific finite value, which can be attributed to classical correlations solely. We further obtain high and low temperature expansions for both quantities. Then, we extend the analysis performed in the seminal paper by Srednicki [ 1 ] for free real scalar field theories in Minkowski space-time in 3 + 1 dimensions at a thermal state. We find that the mutual information obeys an area law, similar to that obeyed by the entanglement entropy at vanishing temperature. The coefficient of this area law does not vanish at infinite temperature. Then, we calculate this coefficient perturbatively in a 1 /μ expansion, where μ is the mass of the scalar field. Finally, we study the high and low temperature behaviour of the area law term.

中文翻译：

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有限温度下自由标量 QFT 互信息的反质量展开

我们研究了有限温度下耦合谐波系统中的纠缠熵和互信息。有趣的是，我们发现互信息在无限温度下不会消失，而是达到特定的有限值，这可以完全归因于经典相关性。我们进一步获得了这两个量的高温和低温膨胀。然后，我们扩展了 Srednicki [1] 在开创性论文中对 Minkowski 时空中 3 + 1 维热状态下的自由实标量场理论进行的分析。我们发现互信息遵循面积定律，类似于消失温度下纠缠熵遵循的面积定律。这个面积定律的系数在无限大的温度下不会消失。然后，我们在 1 /μ 扩展中微扰地计算这个系数，其中 μ 是标量场的质量。最后，我们研究了面积律项的高温和低温行为。