Thermal entangled four-level quantum Otto heat engine

Based on a two-qubit isotropic Heisenberg XXX model with a constant external magnetic field, we construct a four-level entangled quantum heat engine (QHE). The expressions for several thermodynamic quantities such as the heat transferred, the work and efficiency are derived. Moreover, the influence of the entanglement on the thermodynamic quantities is investigated analytically and numerically. Several interesting features of the variation of the heat transferred, the work and the efficiency with the concurrences of the thermal entanglement of different thermal equilibrium states are obtained.