  We investigate the dynamics of bipartite entanglement after the sudden
junction of two leads in interacting integrable models. By combining the
quasiparticle picture for the entanglement spreading with Generalised
Hydrodynamics we derive an analytical prediction for the dynamics of the
entanglement entropy between a finite subsystem and the rest. We find that the
entanglement rate between the two leads depends only on the physics at the
interface and differs from the rate of exchange of thermodynamic entropy. This
contrasts with the behaviour in free or homogeneous interacting integrable
systems, where the two rates coincide.
