# Universal spatial structure of nonequilibrium steady states

## TL;DR

This paper reveals that the large-distance spatial structure of a broad class of nonequilibrium steady states is universal and can be characterized by collective modes, offering insights into their decay and phase transitions.

## Contribution

It introduces the concept of spatial collective modes in NESS, linking their properties to holography and the shear viscosity to entropy ratio, and identifies new nonequilibrium phase transitions.

## Key findings

- Universal spatial decay characterized by collective modes.
- Decay lengths linked to shear viscosity over entropy density ratio.
- Discovery of new nonequilibrium phase transitions.

## Abstract

We describe a large family of nonequilibrium steady states (NESS) corresponding to forced flows over obstacles. The spatial structure at large distances from the obstacle is shown to be universal, and can be quantitatively characterised in terms of certain collective modes of the strongly coupled many body system, which we define in this work. In holography, these modes are spatial analogues of quasinormal modes, which are known to be responsible for universal aspects of relaxation of time dependent systems. These modes can be both hydrodynamical or non-hydrodynamical in origin. The decay lengths of the hydrodynamic modes are set by $\eta/s$, the shear viscosity over entropy density ratio, suggesting a new route to experimentally measuring this ratio. We also point out a new class of nonequilibrium phase transitions, across which the spatial structure of the NESS undergoes a dramatic change, characterised by the properties of the spectrum of these spatial collective modes.