  The quantum Ising chain of length, L, which is separated into two parts by
localized or extended defects is considered at the critical point where scaling
of the interface magnetization is non-universal. We measure the entanglement
entropy between the two halves of the system in equilibrium, as well as after a
quench, when the interaction at the interface is changed for time t>0. For the
localized defect the increase of the entropy with log(L) or with log(t)
involves the same effective central charge, which is a continuous function of
the strength of the defect. On the contrary for the extended defect the
equilibrium entropy is saturated, but the non-equilibrium entropy has a
logarithmic time-dependence the prefactor of which depends on the strength of
the defect.
