Four dynamical regimes of the test-particle quadrupole ZLK problem (assuming ∣j_z∣ ≪ 1). The columns separate the averaging level used (DA on the left; SA on the right), and the rows separate the physics included (no SRFs on top; SRFs on the bottom). Each panel sketches the inner-binary eccentricity e(t) over several secular cycles. Quadrants 1, 2, and 3 represent integrable or near-integrable problems that are well understood (semi)analytically. The focus of this Letter is the fourth quadrant—SA + SRFs—wherein adiabatic invariance is completely broken.