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

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