  Entanglement (EN) is a determinative correlation in designation of quantum
gates and quantum memories. All quantum operations which are assembled by
quantum circuits, are exposed to environment. However, quantum discord (QD) as
a new key of resource for quantum information theory is in spotlight of
research. Therefore, the study of EN and QD in open quantum systems seems to be
important. In this Brief Report, We derived a formula for specific heat of the
principle system as a part of open quantum system (in special for
Jaynes-Cumming regime), and we looked for relations between entanglement and
specific heat which is important for designing of the quantum memory. We also
studied the dynamics of thermal EN and QD in Jaynes-Cumming regime including
the Non-Markovian processes via Born-Markove approximation and obtained a
regions of temperature and coupling constant between parts of systems which the
entanglement of formation had a stable behavior .It seems to be useful to
design the quantum gates. We observed the negative and divergence specific heat
(in contradiction with third law of thermodynamics) in low temperature because
the state of open system is entangle. According to obtained results, we did not
find out any violence oscillation in quantum discord and because entanglement
decreases with respect time, fast response to inputs is crucial for assembling
quantum circuits and quantum memory.
