  A smoking gun signature for a first-order phase transition with negative
speed of sound squared $c_s^2$ is the occurrence of a spinodal instability. In
the gauge/gravity duality it corresponds to a Gregory-Laflamme type
instability, which can be numerically simulated as the evolution of unstable
planar black branes. Making use of holography its dynamics is studied far from
and near a critical point with the following results. Near a critical point the
interface between cold and hot stable phases, given by its width and surface
tension, is found to feature a wider phase separation and a smaller surface
tension. Far away from a critical point the formation time of the spinodal
instability is reduced. Across softer and harder phase transitions, it is
demonstrated that mergers of equilibrated peaks and unstable plateaux lead to
the preferred final single phase separated solution. Finally, a new atypical
setup with dissipation of a peak into a plateau is discovered. In order to
distinguish the inhomogeneous states I propose a new criterium based on the
maximum of the transverse pressure at the interface which encodes phase-mixed
peaks versus fully phase separated plateaux.
