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We study the steady-state entanglement and heat current of two coupled qubits, in which one qubit is connected with either two baths with the different temperature or a bath. We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics and derive the solutions in the steady-state with strong coupling regime between them. We have demonstrated the variations of the steady-state entanglement with respect to various parameters of the system in both equilibrium and nonequilibrium cases. We find that the coupling strengths and the energy detuning as well as the temperature gradient are beneficial to the enhancement of the entanglement in equilibrium case. In the nonequilibrium case, the temperature gradient has different effects on entanglement due to the temperature of the bath(s) which the qubits touch. We also study the heat current and their variations with the energy detuning, coupling strengths and diverse low temperature. The energy detuning has a positive (negative) effect on the heat current in the low (high) temperature; heat current also have different trends with coupling strengths increases for a given temperature. The temperature of cool bath is lower, the heat current is larger.

Q -ordering and P -ordering for the coordinate and momentum operators are introduced, some fundamental identities of Q -ordering and P -ordering P -ordering are derived. the Q -ordered and P -ordered form of the Wigner operator are deduced and Weyl prescription is studied. Moreover, Weyl prescription is developed and perfected.