  Steady-state currents generically occur both in systems with continuous
translation invariance and in nonequilibrium settings with particle drift. In
either case, thermal fluctuations advected by the current act as a source of
noise for slower hydrodynamic modes. This noise is unconventional, since it is
highly correlated along spacetime rays. We argue that, in quasi-one-dimensional
geometries, the correlated noise from ballistic modes generically gives rise to
anomalous full counting statistics (FCS) for diffusively spreading charges. We
present numerical evidence for anomalous FCS in two settings: (1) a
two-component continuum fluid, and (2) the totally asymmetric exclusion process
(TASEP) initialized in a nonequilibrium state.
