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In the 1980s it was theoretically predicted that correlations of variousobservables in a fluid in a non-equilibrium steady state (NESS) areextraordinarily long-ranged, extending, in a well-defined sense, over the sizeof the system. This is to be contrasted with correlations in an equilibriumfluid, whose range is typically just a few particle diameters. These NESScorrelations were later confirmed by numerous experimental studies. Unlikelong-ranged correlations at critical points, these correlations are generic inthe sense that they exist for any temperature as long as the system is in aNESS. In equilibrium systems, generic long-ranged correlations are caused byspontaneously broken continuous symmetries and are associated with ageneralized rigidity, which in turn leads to a new propagating excitation ormode. For example, in a solid, spatial rigidity leads to transverse soundwaves, while in a superfluid, phase rigidity leads to temperature waves knownas second sound at finite temperatures, and phonons at zero temperature. Moregenerally, long-ranged spatial correlations imply rigidity irrespective oftheir physical origin. This implies that a fluid in a NESS should also displaya type of rigidity and related anomalous transport behavior. Here we show thatthis is indeed the case. For the particular case of a simple fluid in aconstant temperature gradient, the anomalous transport behavior takes the formof a super-diffusive spread of a constant-pressure temperature perturbation. Wealso discuss the case of an elastic solid, where we predict a spread that isfaster than ballistic.

Rigidity and Superfast Signal Propagation in Fluids and Solids in Non-Equilibrium Steady States