  We present a quantitative description of the thermalization dynamics of
far-from-equilibrium, two-dimensional (2D) Bose superfluids. Our analysis
leverages a quantum kinetic formalism and allows us to identify two successive
regimes of relaxation: an initial damping of quasi-particles due to Landau
scattering processes, followed by the slower establishment of a global
equilibrium at long time. For a far-from-equilibrium initial state, we find
that Landau damping differs from the conventional picture of exponentially
relaxing quasi-particles. Moreover, our results showcase a pronounced mechanism
of algebraic transport at late times, rooted in energy conservation and
compatible with 2D diffusion. Using theoretical and numerical arguments, we
construct a detailed dynamical portrait of global equilibration in 2D
superfluids.
