Abstract
In this brief report, we attention to the system of two qubits modeled by Heisenberg XXZ chain with the Dzyaloshinskii Moriya interaction. The system exposed to bosonic baths with the Cauchy Lorentz distribution of frequency. We've got a new formula to calculate the specific heat of open systems using density and found that the specific heat at low temperatures can be negative. We observed that when the state of system is entangle, in contradiction with the third law of thermodynamics, the specific heat is diverge when the temperature goes to zero. The speed of divergence is depend to the amount of entanglement. These results may be useful to design solid quantum gate and quantum memories.