We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths of quantum scalar fields at different temperature T ₁ and T ₂ with bilinear couplings between them. We particularly focus on the entanglement or inseparability property of their quantum states. The critical temperatures of two respective oscillators, T _1c and T _2c, higher than which the entanglement disappears, can be determined. It is found that when two damping parameters are largely different, say γ ₁ ≪ γ ₂, the critical temperature T _1c with respect to the frequency Ω₊, the higher frequency among two normal modes frequencies, can be very large, T _1c ≫ Ω₊, while T _2c ∝ Ω₊ with the possibility of hot entanglement. The entanglement of two oscillators with the temperature-dependent damping parameters γ _1;2,T from heat baths is also discussed.

我们研究了两个耦合振荡器在不同温度T ₁和T ₂下与它们自己的量子标量场热浴相互作用的非平衡动力学，它们之间存在双线性耦合。我们特别关注它们的量子态的纠缠或不可分离性。可以确定两个各自的振荡器的临界温度T _1c和T _2c，高于纠缠消失的温度。发现当两个阻尼参数相差很大时，比如γ ₁ ≪ γ ₂，临界温度T _1c相对于频率 Ω₊，两个正常模式频率中较高的频率，可以非常大，T _1c ≫ Ω ₊，而T _2c ∝ Ω ₊具有热纠缠的可能性。还讨论了两个振荡器的纠缠与温度相关的阻尼参数γ _{1; 2, T} 来自热浴。