  Thermal equilibrium states of local quantum many-body systems are notorious
for their spatially decaying correlations, which place severe restrictions on
the types of many-body entanglement structures that may be observed at finite
temperatures. These restrictions may however be defied when an
out-of-equilibrium steady state is considered instead. In this paper, we study
the entanglement properties of free fermions on a one-dimensional lattice that
contains a generic charge- and energy-conserving noninteracting impurity, and
that is connected at its edges to two reservoirs with different equilibrium
energy distributions. These distributions may differ in either temperature,
chemical potential, or both, thereby inducing an external bias. We analytically
derive exact asymptotic expressions for several quantum information measures --
the mutual information, its R\'enyi generalizations, and the fermionic
negativity -- that quantify the correlation and entanglement between two
subsystems located on opposite sides of the impurity. We show that all these
measures scale (to a leading order) linearly with the overlap between one
subsystem and the mirror image of the other (upon reflection of the latter
about the impurity), independently of the distance between the subsystems.
While a simple proportionality relation between the negativity and R\'enyi
versions of the mutual information is observed to hold at zero temperature, it
breaks down at finite temperatures, suggesting that these quantities represent
strong long-range correlations of different origins. Our results generalize
previous findings that were limited to the case of a chemical-potential bias at
zero temperature, rigorously demonstrating that the effect of long-range
volume-law entanglement is robust at finite temperatures.
