Non-equilibrium steady state formation in 3+1 dimensions

We present the first holographic simulations of non-equilibrium steady state formation in strongly coupled $\mathcal{N}=4$ SYM theory 3+1 dimensions. initially join together two thermal baths at different temperatures and chemical potentials compare subsequent evolution combined system to analytic solutions corresponding Riemann problem numeric ideal viscous hydrodynamics. The time energy density that we obtain holographically is consistent with combination a shock rarefaction wave: A wave moves towards cold bath, smooth broadening hot bath. Between waves emerges constant temperature flow velocity, both which are accurately described by shock+rarefaction solution problem. In region, crossover develops between regions charge density. This reminiscent contact discontinuity also results for entanglement entropy crossed find them closely follow