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

TL;DR

This paper explores how non-equilibrium steady states in fluids and solids exhibit long-range correlations and rigidity, leading to superfast signal propagation and anomalous transport behaviors.

Contribution

It demonstrates that fluids in NESS show rigidity and superdiffusive behavior, extending the concept of long-range correlations and propagating modes beyond equilibrium systems.

Findings

Fluid in NESS exhibits superdiffusive temperature perturbation spread.

Elastic solids show faster-than-ballistic signal propagation.

Long-range correlations imply rigidity in non-equilibrium conditions.

Abstract

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.