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. They exhibit traveling wave solutions that are
discontinuous at the boundary of the light cone, and have a perfectly causal
structure where the solutions do not spill outside of the light cone.Comment: 31 pages, 7 figure