  We consider an analytically tractable model that exhibits the main features
of the Page curve characterizing the evolution of entanglement entropy during
evaporation of a black hole. Our model is a gas of non-interacting fermions on
a lattice that is released from a box into the vacuum. More precisely, our
Hamiltonian is a tight-binding model with a defect at the junction between the
filled box and the vacuum. In addition to the entanglement entropy we consider
several other observables, such as the spatial density profile and current, and
show that the semiclassical approach of generalized hydrodynamics provides a
remarkably accurate description of the quantum dynamics including that of the
entanglement entropy at all times. Our hydrodynamic results agree closely with
those obtained via exact microscopic numerics. We find that the growth of
entanglement is linear and universal, i.e, independent of the details of the
defect. The decay shows $1/t$ scaling for conformal defect while for
non-conformal defects, it is slower. Our study shows the power of the
semiclassical approach and could be relevant for discussions on the resolution
of the black hole information paradox.
