  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.
