Nonequilibrium thermal entanglement

Results on heat current, entropy production rate, and entanglement are reported for a quantum system coupled to two different temperature heat reservoirs. By applying a temperature gradient, different quantum states can be found with exactly the same amount of entanglement but different purity degrees and heat currents. Furthermore, a nonequilibrium enhancement-suppression transition behavior of the entanglement is identified.

Figure 1

(Color online) Quantum-state parameter space $(e_1,e_2)$. The black line denotes equilibrium states. Green line: entangled-unentangled border for $ϵ<1$. Red line: entangled-unentangled border for $ϵ>1$. Circles represent the state shift under a temperature gradient from the same mean temperature $T_M=1$. Blue circles: $ϵ=1∕3$. Brown circles: $ϵ=3$.

Figure 2

(Color online) LNEL coefficients $\alpha$ and ${\alpha }^{\prime }$, denoting the second order in $\Delta T$ variation of the concurrence and linear entropy, respectively: (a) $ϵ=3$, (b) $ϵ=1∕3$. Insets: equilibrium concurrence.

Figure 3

(Color online) Heat current $\mathcal{J}$ and concurrence evolution for different mean temperatures $T_M$. Inset: linear entropy and concurrence. Each point corresponds to a $\Delta T$ value.

Figure 4

(Color online) Thermodynamical entropy production rate and concurrence evolutions for different mean temperatures $T_M$. Each point corresponds to a $\Delta T$ value.

Figure 5

(Color online) Heat current $\mathcal{J}$ and concurrence evolution for different mean temperatures $T_M$ in the nonsymmetric case, ${ϵ}_1=8$ and ${ϵ}_2=3$. Inset ${ϵ}_1=3$ and ${ϵ}_2=8$. Each point corresponds to a $\Delta T$ value.