Dynamics of holographic steady flows near a first-order phase transition

We investigate the physical properties of steady flows in a holographic first-order phase transition model, extending from the thermodynamics at equilibrium to the real-time dynamics far from equilibrium. Through spinodal decomposition or condensation nuclei, the phase-separated state with non-zero momentum can be achieved. In this scenario, we observe a gap between coexisting phases, arising not only from the variations in energy density, but also from the distinctions in momentum density or longitudinal pressure. These disparities are characterized by flow velocity and latent heat. Furthermore, by introducing an inhomogeneous scalar external source to simulate a fixed obstacle, we reveal the dynamical response of momentum loss in the moving system. Notably, starting from an initial phase-separated state with uniform flow velocity, and subsequently interacting it with an obstacle, we find that the moving high-energy phase exhibits four characteristic dynamical behaviors -- rebounding, pinning, passing, and splitting. These behaviors depend on the velocity of the phase and the strength of the obstacle.