  We present the contribution from potential interactions to the dynamics of
non-spinning binaries to fourth Post-Minkowskian (4PM) order. This is achieved
by computing the scattering angle to ${\cal O}(G^4)$ using the effective field
theory approach and deriving the bound radial action through analytic
continuation. We reconstruct the Hamiltonian and center-of-mass momentum in an
isotropic gauge. The (three-loop) integrals involved in our calculation are
computed via differential equations, including a sector yielding elliptic
integrals. Using the universal link between potential and tail terms, we also
report: 1) The instantaneous energy flux at ${\cal O}(G^3)$; 2) The
contribution to the 4PM unbound/bound radial action(s) depending on logarithms
of the binding energy; 3) The (scheme-independent) logarithmic contribution to
the 4PM non-local tail Hamiltonian for circular orbits. Our results in the
potential region are in agreement with the recent derivation from scattering
amplitudes. We also find perfect agreement in the overlap with the
state-of-the-art in Post-Newtonian theory.
