  We study the propagation of entanglement after quantum quenches in the
non-integrable para-magnetic quantum Ising spin chain. Tuning the parameters of
the system, we observe a sudden increase in the entanglement production rate,
which we show to be related to the appearance of new quasi-particle excitations
in the post-quench spectrum. We argue that the phenomenon is the
non-equilibrium version of the well-known Gibbs paradox related to mixing
entropy and demonstrate that its characteristics fit the expectations derived
from the quantum resolution of the paradox in systems with a non-trivial
quasi-particle spectrum.
