  Out-of-equilibrium states of many-body systems tend to evade a description by
standard statistical mechanics, and their uniqueness is epitomized by the
possibility of certain long-range correlations that cannot occur in
equilibrium. In quantum many-body systems, coherent correlations of this sort
may lead to the emergence of remarkable entanglement structures. In this work,
we analytically study the asymptotic scaling of quantum correlation measures --
the mutual information and the fermionic negativity -- within the
zero-temperature steady state of voltage-biased free fermions on a
one-dimensional lattice containing a noninteracting impurity. Previously, we
have shown that two subsystems on opposite sides of the impurity exhibit
volume-law entanglement, which is independent of the absolute distances of the
subsystems from the impurity. Here we go beyond that result and derive the
exact form of the subleading logarithmic corrections to the extensive terms of
correlation measures, in excellent agreement with numerical calculations. In
particular, the logarithmic term of the mutual information asymptotics can be
encapsulated in a concise formula, depending only on simple four-point ratios
of subsystem length-scales and on the impurity scattering probabilities at the
Fermi energies. This echoes the case of equilibrium states, where such
logarithmic terms may convey universal information about the physical system.
To compute these exact results, we devise a hybrid method that relies on
Toeplitz determinant asymptotics for correlation matrices in both real space
and momentum space, successfully circumventing the inhomogeneity of the system.
This method can potentially find wider use for analytical calculations of
entanglement measures in similar scenarios.
