  We investigate the out-of-equilibrium properties of a simple quantum impurity
model, the interacting resonant level model (IRLM). We focus on the scaling
regime, where the bandwidth of the fermions in the leads is larger than all the
other energies, so that the lattice and the continuum versions of the model
become equivalent. Using time-dependent DMRG simulations initialized with
states having different densities in the two leads we extend the results of
Boulat, Saleur and Schmitteckert [Phys. Rev. Lett. 101, 140601 (2008)]
concerning the current-voltage ($I$-$V$) curves, for several values of the
interaction strength $U$. We estimate numerically the Kondo scale $T_B$ and the
exponent $b(U)$ associated to the tunneling of the fermions from the leads to
the dot. Next we analyze the quantum entanglement properties of the steady
states. We focus in particular on the entropy rate $\alpha$, describing the
linear growth with time of the bipartite entanglement in the system. We show
that, as for the current, $\alpha/T_B$ is described by some function of $U$ and
of the rescaled bias $V/T_B$. Finally, the spatial structure of the entropy
profiles is discussed.
