Entanglement dynamics of an open two-qubit anisotropic XY Heisenberg system is investigated in the presence of an inhomogeneous magnetic field and spin-orbit interaction. We suppose that each qubit interacts with a separate thermal reservoir which is held in its own temperature. The asymptotical and the dynamical behavior of entanglement are analyzed. To distinguish between entanglement induced by the environment and entanglement due to the presence of inter-qubit interaction, the effects of spin-orbit parameter D and temperature difference parameter ΔT on the entanglement of the system have been investigated. We show that for a fixed set of the system parameters, entanglement can be produced just by adjusting the temperature difference between the reservoirs. The size of this entanglement, which is induced by temperature difference of reservoirs, increases as the spin-orbit parameter D increases. Also we find that, this environment induced entanglement can be improved if the qubit influenced by the weaker magnetic field is in contact with the hotter reservoir, i.e. indirect geometry of connection. In this case, the amount of asymptotic entanglement increases as D increases. Regardless of the geometry of connection, increasing D causes the appearance of entanglement in the larger regions of TM − ΔT plane, therefore entanglement can exist in higher temperatures and temperature differences. Furthermore, increasing D enhances the amount of entanglement in these regions. We also show that the state of the system can be found in the maximally entangled state for the case of zero temperature reservoirs and large amount of the spin-orbit parameter.

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