  In certain analytically-tractable quantum chaotic systems, the calculation of
out-of-time-order correlation functions, entanglement entropies after a quench,
and other related dynamical observables, reduces to an effective theory of an
``entanglement membrane'' in spacetime. These tractable systems involve an
average over random local unitaries defining the dynamical evolution. We show
here how to make sense of this membrane in more realistic models, which do not
involve an average over random unitaries. Our approach relies on introducing
effective pairing degrees of freedom in spacetime, describing a pairing of
forward and backward Feynman trajectories, inspired by the structure emerging
in random unitary circuits. This provides a framework for applying ideas of
coarse-graining to dynamical quantities in chaotic systems. We apply the
approach to some translationally invariant Floquet spin chains studied in the
literature. We show that a consistent line tension may be defined for the
entanglement membrane, and that there are qualitative differences in this
tension between generic models and ``dual-unitary'' circuits. These results
allow scaling pictures for out-of-time-order correlators and for entanglement
to be taken over from random circuits to non-random Floquet models. We also
provide an efficient numerical algorithm for determining the entanglement line
tension in 1+1D.
