  We study the quantum information spreading in one-dimensional free-fermion
systems in the presence of localized thermal baths. We employ a nonlocal
Lindblad master equation to describe the system-bath interaction, in the sense
that the Lindblad operators are written in terms of the Bogoliubov operators of
the closed system, and hence are nonlocal in space. The statistical ensemble
describing the steady state is written in terms of a convex combination of the
Fermi-Dirac distributions of the baths. Due to the singularity of the
free-fermion dispersion, the steady-state mutual information exhibits
singularities as a function of the system parameters. While the mutual
information generically satisfies an area law, at the singular points it
exhibits logarithmic scaling as a function of subsystem size. By employing the
Fisher-Hartwig theorem, we derive the prefactor of the logarithmic scaling,
which depends on the parameters of the baths and plays the role of an effective
"central charge". This is upper bounded by the central charge governing
ground-state entanglement scaling. We provide numerical checks of our results
in the paradigmatic tight-binding chain and the Kitaev chain.
