Crossing a large-N phase transition at finite volume

The existence of phase-separated states is an essential feature infinite-volume systems with a thermal, first-order phase transition. At energies between those at which the transition takes place, equilibrium homogeneous are either metastable or suffer from spinodal instability. In this range stable inhomogeneous, states. We use holography to investigate how picture modified finite volume in strongly coupled, four-dimensional gauge theory. work planar limit, $N \to \infty$, ensures that we remain thermodynamic limit. uncover rich set inhomogeneous dual lumpy black branes on gravity side, as well first- and second-order transitions them. establish their local (in)stability properties show fully non-linear time evolution bulk unstable ones.