  Recently an effective membrane theory valid in a "hydrodynamic limit" was
proposed to describe entanglement dynamics of chaotic systems based on results
in random quantum circuits and holographic gauge theories. In this paper, we
show that this theory is robust under a large set of generalizations. In
generic quench protocols we find that the membrane couples geometrically to
hydrodynamics, joining quenches are captured by branes in the effective theory,
and the entanglement of time evolved local operators can be computed by probing
a time fold geometry with the membrane. We also demonstrate that the structure
of the effective theory does not change under finite coupling corrections
holographically dual to higher derivative gravity and that subleading orders in
the hydrodynamic expansion can be incorporated by including higher derivative
terms in the effective theory.
