  How quantum information is scrambled in the global degrees of freedom of
non-equilibrium many-body systems is a key question to understand local
thermalization. Here we propose that the scaling of the mutual information
between two intervals of fixed length as a function of their distance is a
diagnostic tool for scrambling after a quantum quench. We consider both
integrable and non-integrable one dimensional systems. In integrable systems,
the mutual information exhibits an algebraic decay with the distance between
the intervals, signalling weak scrambling. This behavior may be qualitatively
understood within the quasiparticle picture for the entanglement spreading,
predicting, in the scaling limit of large intervals and times, a decay exponent
equal to $1/2$. Away from the scaling limit, the power-law behavior persists,
but with a larger (and model-dependent) exponent. For non-integrable models, a
much faster decay is observed, which can be attributed to the finite life time
of the quasiparticles: unsurprisingly, non-integrable models are better
scramblers.
