  We study the radial acceleration relation (RAR) between the total ($a_{\rm
tot}$) and baryonic ($a_{\rm bary}$) centripetal acceleration profiles of
central galaxies in the cold dark matter (CDM) paradigm. We analytically show
that the RAR is intimately connected with the physics of the quasi-adiabatic
relaxation of dark matter in the presence of baryons in deep potential wells.
This cleanly demonstrates how a near-universal mean RAR and its scatter emerges
in the low-acceleration regime ($10^{-12}\,{\rm m\,s}^{-2}\lesssim a_{\rm
bary}\lesssim10^{-10}\,{\rm m\,s}^{-2}$) from an interplay between baryonic
feedback processes and the distribution of CDM in dark halos. Our framework
allows us to go further and study both higher and lower accelerations in
detail, using analytical approximations and a realistic mock catalog of
$\sim342,000$ low-redshift central galaxies with $M_r\leq-19$. We show that,
while the RAR in the baryon-dominated, high-acceleration regime ($a_{\rm
bary}\gtrsim10^{-10}\,{\rm m\,s}^{-2}$) is very sensitive to details of the
relaxation physics, a simple `baryonification' prescription matching the
relaxation results of hydrodynamical CDM simulations is remarkably successful
in reproducing the observed RAR without any tuning. And in the (currently
unobserved) ultra-low-acceleration regime ($a_{\rm bary}\lesssim 10^{-12}\,{\rm
m\,s}^{-2}$), the RAR is sensitive to the abundance of diffuse gas in the halo
outskirts, with our default model predicting a distinctive break from a simple
power-law-like relation for HI-deficient, diffuse gas-rich centrals. Our mocks
also show that the RAR provides more robust, testable predictions of the
$\Lambda$CDM paradigm at galactic scales, with implications for alternative
gravity theories, than the baryonic Tully-Fisher relation.
