  In the 1980s it was theoretically predicted that correlations of various
observables in a fluid in a non-equilibrium steady state (NESS) are
extraordinarily long-ranged, extending, in a well-defined sense, over the size
of the system. This is to be contrasted with correlations in an equilibrium
fluid, whose range is typically just a few particle diameters. These NESS
correlations were later confirmed by numerous experimental studies. Unlike
long-ranged correlations at critical points, these correlations are generic in
the sense that they exist for any temperature as long as the system is in a
NESS. In equilibrium systems, generic long-ranged correlations are caused by
spontaneously broken continuous symmetries and are associated with a
generalized rigidity, which in turn leads to a new propagating excitation or
mode. For example, in a solid, spatial rigidity leads to transverse sound
waves, while in a superfluid, phase rigidity leads to temperature waves known
as second sound at finite temperatures, and phonons at zero temperature. More
generally, long-ranged spatial correlations imply rigidity irrespective of
their physical origin. This implies that a fluid in a NESS should also display
a type of rigidity and related anomalous transport behavior. Here we show that
this is indeed the case. For the particular case of a simple fluid in a
constant temperature gradient, the anomalous transport behavior takes the form
of a super-diffusive spread of a constant-pressure temperature perturbation. We
also discuss the case of an elastic solid, where we predict a spread that is
faster than ballistic.
