Entanglement of quantum oscillators coupled to different heat baths

We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths quantum scalar fields at different temperature $T_1$ and $T_2$ bilinear couplings between them. particularly focus on entanglement or inseparability property states. The critical temperatures respective oscillators, $T_{1c}$ $T_{2c}$, higher than which disappears, can be determined. It is found that when damping parameters are largely different, say $\gamma_1 \ll \gamma_2$, respect to frequency $\Omega_+$, among normal modes frequencies, very large, $T_{1c} \gg \Omega_+$, while $T_{2c} \propto \Omega_+$ possibility hot entanglement. temperature-dependent $\gamma_{1;2,T}$ from also discussed.