  We demonstrate that 2D Fermi liquids can support peculiar excitations that
are not subject to Landau's $T^2$ dissipation. The long-lived excitations relax
through correlated angular dynamics involving "lock-step" angular displacements
along the Fermi surface occurring in collinear two-particle collisions, a
surprising behavior that is unique to 2D systems. We develop a microscopic
picture of the non-Brownian random walk, describing the angular dynamics as
anomalous diffusion ("superdiffusion") on the Fermi surface.
Strongly-correlated dynamics with directional memory, mediated by novel
undamped excitations, dominates at moderately long times, pushing the onset of
conventional hydrodynamics to abnormally large timescales. This exotic behavior
can be directly probed by momentum-resolved tunneling techniques.
