A special entangled quantum heat engine based on the two-qubit Heisenberg XX model

We construct a special four-level entangled quantum Otto heat engine based on the two-qubit Heisenberg X X model, in which we assume that all the energy gaps are changed in the same ratio in the two quantum adiabatic processes. Hence during the whole cycle, the relative coupling constant kappa = J/B is fixed, where J and B are the coupling constant and the external magnetic field, respectively. The dependence of the basic thermodynamical quantities on the two entanglements at the end of two quantum isochoric processes with different relative coupling constants kappa is studied. Our results show that in the weak coupling region, i.e. kappa < 1, the heat engine can be operated in both areas where c(1) < c(2) and c(1) > c(2), whereas when kappa >= 1, it only operates under the condition c(1) < c(2). Here c(1) and c(2) are entanglements of the working substance when it comes into contact with hot and cold baths, respectively. Moreover, we find that the maximal work output for fixed kappa increases with the relative coupling constant.