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The LIGO/Virgo detections of compact object mergers have posed a challengefor theories of binary evolution and coalescence. One promising avenue forproducing mergers dynamically is through secular eccentricity oscillationsdriven by an external perturber, be it a tertiary companion (as in theLidov-Kozai (LK) mechanism) or the tidal field of the stellar cluster in whichthe binary orbits. The simplest theoretical models of these oscillations use a'doubly-averaged' (DA) approximation, averaging both over the binary's internalKeplerian orbit and its 'outer' barycentric orbit relative to the perturber.However, DA theories do not account for fluctuations of the perturbing torqueon the outer orbital timescale, which are known to increase a binary'seccentricity beyond the maximum DA value, potentially accelerating mergers.Here we reconsider the impact of these short-timescale fluctuations in thetest-particle quadrupolar limit for binaries perturbed by arbitrary sphericalcluster potentials (including LK as a special case), {in particular including1pN} general relativistic (GR) apsidal precession of the internal orbit.Focusing on the behavior of the binary orbital elements around peakeccentricity, we discover a new effect, relativistic phase space diffusion(RPSD), in which a binary can jump to a completely new dynamical trajectory onan outer orbital timescale, violating the approximate conservation of DAintegrals of motion. RPSD arises from an interplay between secular behavior atextremely high eccentricity, short-timescale fluctuations, and rapid GRprecession, and can change the subsequent secular evolution dramatically. Thiseffect occurs even in hierarchical triples, but has not been uncovered untilnow.

Relativistic phase space diffusion of compact object binaries in stellar clusters and hierarchical triples