Abstract

In comparison to the well-established subject of equilibrium thermodynamics, physics out of equilibrium is much less understood. The field is vast, but a family of states that have the potential for a powerful theoretical description is that of non-equilibrium steady states. These do not change macroscopically with time, but support steady flows, be it of charges, particles, or energy. They naturally generalize equilibrium thermodynamic states, and can be truly far from equilibrium, with entropy production. There has been a lot of progress in their study within classical dynamics, and more recently quantum dynamics. In many-body quantum systems this is especially interesting because of the nontrivial interplay between non-equilibrium physics and many-body behaviours, such as those captured by quantum field theory or those associated to integrability. I will describe some of the main ideas, focussing on exact results for far-from-equilibrium ballistic transport especially at or near criticality. As I will explain, a variety of fundamental aspects of many-body physics turn out to play important roles: the Lieb-Robinson bound for the velocity of propagation of information, chiral factorization in one dimension, (generalized) local Gibbs thermalization and the eigenstate thermalization hypothesis, shock waves and fluid dynamics, and gauge-gravity duality. This is based on works done in collaborations with Denis Bernard, Marianne Hoogeveen, and Joe Bhaseen, Andrew Lucas and Koenraad Schalm.