  We study the reduced dynamics of open quantum spin chains of arbitrary length
$N$ with nearest neighbour $XX$ interactions, immersed within an external
constant magnetic field along the $z$ direction, whose end spins are weakly
coupled to heat baths at different temperatures, via energy preserving
couplings. We find the analytic expression of the unique stationary state of
the master equation obtained in the so-called global approach based on the
spectralization of the full chain Hamiltonian. Hinging upon the explicit
stationary state, we reveal the presence of sink and source terms in the
spin-flow continuity equation and compare their behaviour with that of the
stationary heat flow. Moreover, we also obtain analytic expressions for the
steady state two-spin reduced density matrices and for their concurrence. We
then set up an algorithm suited to compute the stationary bipartite
entanglement along the chain and to study its dependence on the Hamiltonian
parameters and on the bath temperatures.
