  The LIGO/Virgo detections of compact object mergers have posed a challenge
for theories of binary evolution and coalescence. One promising avenue for
producing mergers dynamically is through secular eccentricity oscillations
driven by an external perturber, be it a tertiary companion (as in the
Lidov-Kozai (LK) mechanism) or the tidal field of the stellar cluster in which
the binary orbits. The simplest theoretical models of these oscillations use a
'doubly-averaged' (DA) approximation, averaging both over the binary's internal
Keplerian orbit and its 'outer' barycentric orbit relative to the perturber.
However, DA theories do not account for fluctuations of the perturbing torque
on the outer orbital timescale, which are known to increase a binary's
eccentricity beyond the maximum DA value, potentially accelerating mergers.
Here we reconsider the impact of these short-timescale fluctuations in the
test-particle quadrupolar limit for binaries perturbed by arbitrary spherical
cluster potentials (including LK as a special case), {in particular including
1pN} general relativistic (GR) apsidal precession of the internal orbit.
Focusing on the behavior of the binary orbital elements around peak
eccentricity, we discover a new effect, relativistic phase space diffusion
(RPSD), in which a binary can jump to a completely new dynamical trajectory on
an outer orbital timescale, violating the approximate conservation of DA
integrals of motion. RPSD arises from an interplay between secular behavior at
extremely high eccentricity, short-timescale fluctuations, and rapid GR
precession, and can change the subsequent secular evolution dramatically. This
effect occurs even in hierarchical triples, but has not been uncovered until
now.
