Figure 1

(Color online) Three cycles of the heat engine in the $(\omega ,{\mathcal{S}}_E)$ plane (dimensional units $\hslash =1,k_b=1$). The common values are: $J=2.0$, $T_h=7.5$, $T_c=1.5$, ${\omega }_a=5.08364$, ${\omega }_b=12.6355$, heat-transfer rates ${\Gamma }_h={\Gamma }_c=1.16748$, and dephasing rates ${\gamma }_h=-0.05$, ${\gamma }_c=-0.06$. ${\Lambda }_{ba}={\Lambda }_{ab}=0$ [Eq. (11)] for the unlubricated cycle (black), ${\Lambda }_{ba}=1.28$, ${\Lambda }_{ab}=0.64$ for the intermediate cycle (red), and ${\Lambda }_{ba}=122.88$, ${\Lambda }_{ab}=61.44$ for the strongly lubricated cycle (green). The time allocations on the different branches correspond to the optimal engine’s power, when ${\Lambda }_{ba}={\Lambda }_{ab}=0$. The optimal time allocations are ${\tau }_h=1.0795,{\tau }_{ba}=0.01478$, ${\tau }_c=1.0088$, and ${\tau }_{ab}=0.0069$. The points $\mathbf{E}$ and $\mathbf{F}$ represent the equilibrium points of the hot and cold isochores.Reuse & Permissions

Figure 2

(Color online) The optimal power $\mathcal{P}$ as function of cycle time $\tau$ with and without the quantum lubricant. The optimization is with respect to the time allocations for ${\Lambda }_{ba}={\Lambda }_{ab}=0$ (lower line). The power with the lubrication ${\Lambda }_{ba}=1.28{\Lambda }_{ab}=0.64$ (top line). All the other parameters are as in Fig. 1.Reuse & Permissions

Figure 3

(Color online) The work performed by the engine on the adiabat $b\to a$ branch, separated into $W^{friction}$ (left scale) and $W^{field}$ (right scale) for different dephasing values as a function of ${\Omega }_{ba}\left(t\right)$. $W^{field}$ has only a weak dependence on the dephasing lubricating value $\Lambda$. The cycle parameter values are as in Fig. 1.Reuse & Permissions

Figure 4

(Color online) Power (right scale, red online) and entropy production (left scale, blue online) as a function of the dephasing parameter ${\Lambda }_{ab}^{1∕2}$ and the variance, ${\sigma }_{ab}$ of the random fluctuations of the time segment on the adiabats (upper scale). The dephasing synthesis results are represented by stars and filled triangles. The empty circles and squares represent the dephasing dynamics. The calculations were performed with ${\Lambda }_{ab}∕{\Lambda }_{ba}={\sigma }_{ab}∕{\sigma }_{ba}$.Reuse & Permissions