  We investigate the behavior of entanglement between a single fermionic level
and a fermionic bath in three distinct thermodynamic regimes. First, in thermal
equilibrium, we analyze the dependence of entanglement on the considered
statistical ensemble: for the grand canonical state, it is generated only for a
sufficiently strong system-bath coupling, whereas it is present for arbitrarily
weak couplings for the canonical state with a fixed particle number. The
threshold coupling strength, at which entanglement appears, is shown to
strongly depend on the bath bandwidth. Second, we consider the relaxation to
equilibrium. In this case a transient entanglement in a certain time interval
can be observed even in the weak-coupling regime, when the reduced dynamics and
thermodynamics of the system can be well described by an effectively classical
and Markovian master equation for the state populations. At strong coupling
strengths, entanglement is preserved for long times and converges to its
equilibrium value. Finally, in voltage-driven junctions, a steady-state
entanglement is generated for arbitrarily weak system-bath couplings at a
certain threshold voltage. It is enhanced in the strong-coupling regime, and it
is reduced by either the particle-hole or the tunnel coupling asymmetry.
