Evaluating the performance of a refrigerator by an external system using entanglement

We propose a model of a quantum thermal refrigeration machine interacting with an external atom via an entanglement phenomenon. The machine is formed by three qubits of two-level, where each one interacts locally with its proper reservoir at different temperatures. The second qubit of the refrigerator and the external qubit are initially prepared in an entangled state. The effect of the quantum refrigerator on the entanglement of the final atomic state is studied. It is shown that the survival of the entanglement of the atomic system (Qubits 2 and 4) depends on the temperature of the second reservoir. The heat flow from the cold bath (cooling power) to the hot bath is discussed, where we prove that the refrigeration may be enhanced by the energy coming from the entangled external qubit. Indeed, it is shown that the enhancement of cooling power by increasing the degree of entanglement.