The non-equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation-dissipation relation is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero-point fluctuations. No rotating-wave approximation is applied, and anomalous heat transport from cold to hot bath, as reported in earlier work, is demonstrated not to occur.

中文翻译：

---

两个量子振荡器的传热和纠缠-非平衡相关光谱

讨论了两个相互相互作用并耦合到单独热浴的振荡器的非平衡状态。考虑了玻色浴，并通过分析提供了协方差矩阵元素的精确光谱表示。允许用于相关浴模式的多种光谱密度。波动-耗散关系的有效性是针对静止状态下的全局平衡（两个浴槽温度相同）建立的。通过与零点波动的平衡谱进行比较，提出了纠缠的谱测量。没有应用旋转波近似，并且证明没有发生从冷浴到热浴的异常热传递，正如早期工作中所报告的那样。