Scrambling in the memory matrix formalism; quantum information as a hydrodynamical slow mode.

Quantum information is conserved under unitary dynamics, and can be viewed as a hydrodynamical slow mode. We re-frame operator spreading within the memory matrix formalism (MMF) by including this often overlooked slow mode. This formalism yields a succinct expression for the butterfly velocity and shows that the biased diffusion of operators in ergodic systems is arguably the simplest scenario consistent with unitary dynamics. We use this formalism to present non-perturbative results for a Floquet circuit without symmetry and discuss the inplications of additional conserved quantities on scrambling.