  Stabilizer entropies (SE) measure deviations from stabilizer resources and as
such are a fundamental ingredient for quantum advantage. In particular, the
interplay of SE and entanglement is at the root of the complexity of
classically simulating quantum many-body systems. In this paper, we study the
dynamics of SE in a quantum many-body system away from the equilibrium after a
quantum quench in an integrable system. We obtain two main results: (i) we show
that SE, despite being an L-extensive quantity, equilibrates in a time that
scales at most linearly with the subsystem size; and (ii) we show that there is
a SE length increasing linearly in time, akin to correlations and entanglement
spreading.
