  We formulate a kinetic theory of quantum information scrambling in the
context of a paradigmatic model of interacting electrons in the vicinity of a
superconducting phase transition. We carefully derive a set of coupled partial
differential equations that effectively govern the dynamics of information
spreading in generic dimensions. Their solutions show that scrambling
propagates at the maximal speed set by the Fermi velocity. At early times, we
find exponential growth at a rate set by the inelastic scattering. At late
times, we find that scrambling is governed by shock-wave dynamics with
traveling waves exhibiting a discontinuity at the boundary of the light cone.
Notably, we find perfectly causal dynamics where the solutions do not spill
outside of the light cone.
