In this talk I will present the first holographic simulations of non-equilibrium steady state formation in strongly coupled N=4 SYM theory in 3+1 dimensions . This is achieved by joining together two thermal baths at different temperatures and chemical potentials and comparing the subsequent evolution of the combined system to analytic solutions of the corresponding Riemann problem and to numeric solutions of ideal and viscous hydrodynamics. The time evolution of the energy density that we obtain holographically is consistent with the combination of a shock and a rarefaction wave: A shock wave moves towards the cold bath, and a smooth broadening wave towards the hot bath. Between the two waves emerges a steady state with constant temperature and flow velocity.
Time permitting there will be a somewhat different topic in a similar set-up, where we consider a boundary FRW theory with dynamical gravity . This will give a short introduction to how to have an evolution scheme that allows to evolve far-from-equilibrium strongly coupled matter on a background that evolves according to the Einstein equations.
 Christian Ecker, Johanna Erdmenger and WS, Non-equilibrium steady state formation in 3+1 dimensions, 2103.10435 (SciPost Phys)
 Christian Ecker, WS, David Mateos and Jorge Casalderrey-Solana, Holographic Evolution with Dynamical Boundary Gravity, 2109.10355