What are the mechanisms at play in the spontaneous imbibition dynamics in polyethylene terephthalate filament yarns at pore scale? Processes at pore scale such as waiting times between the filling of two neighboring pores, as observed in special irregular porous media, like yarns, may overrule the predicted behavior by well-known laws such as Washburn's law. While the imbibition physics are well known, classic models like Washburn's law cannot explain the dynamics observed for yarns. The stepwise dynamics is discussed in terms of the interplay of thermodynamic free energy and viscous dissipation. Time-resolved synchrotron x-ray microtomography documents water filling at pore scale. Spontaneous imbibition in yarns is characterized by a series of fast pore-filling events separated by long periods of low flux. Four-dimensional imaging allows the extraction of interface areas at the boundaries between water, air, and polymer and the calculation of free-energy evolution. It is found that the waiting periods correspond to quasistable water configurations of almost vanishing free-energy gradient. The distributions of pore filling event sizes and waiting times spread over several orders of magnitude, resulting in the pronounced stepwise uptake dynamics.