  We study the orbital evolution of hierarchical quadruple systems composed of
two binaries on a long mutual orbit, where each binary acts as a Kozai-Lidov
(KL) perturber on the other. We find that the coupling between the two binaries
qualitatively changes the behavior of their KL cycles. The binaries can
experience coherent eccentricity oscillations as well as excursions to very
high eccentricity that occur over a much larger fraction of the parameter space
than in triple systems. For a ratio of outer to inner semi-major axes of 10 to
20, about 30 to 50% of equal-mass quadruples reach eccentricity 1-e < 10^{-3}
in one of the binaries. This is about 4 to 12 times more than for triples with
equivalent parameters. Orbital "flips" and collisions without previous tidal
interaction are similarly enhanced in quadruples relative to triples. We argue
that the frequency of evolutionary paths influenced by KL cycles is comparable
in the triple and quadruple populations even though field quadruples are a
factor of ~5 less frequent than triples. Additionally, quadruples might be a
non-negligible source of triples and provide fundamentally new evolutionary
outcomes involving close binaries, mergers, collisions, and associated
transients, which occur without any fine tuning of parameters. Finally, we
study the perturbations to a planetary orbit due to a distant binary and we
find that the fraction of orbital flips is a factor of 3 to 4 higher than for
the corresponding triple system given our fiducial parameters with implications
for hot Jupiters and star-planet collisions.
