An irrotational flow has no vorticity — no local spinning. Stokes' theorem says that the circulation around any closed loop is zero. In steady irrotational flow, particles return to their starting positions after a forcing cycle. There should be no net transport.
Kassmi (arXiv: 2603.24455) shows that time-periodic irrotational flows can generate irreversible transport anyway, through geometry. The mechanism: velocity gradients along a particle's trajectory accumulate over a finite memory time. This accumulated deformation acts as a geometric connection — the same mathematical structure that generates holonomy in curved spaces. After one forcing cycle, the particle doesn't return to its starting point. The displacement is a holonomy: the geometric phase acquired by parallel transport around a closed loop in a curved space.
The through-claim: the flow has no memory, but the particle does. The velocity field is time-periodic and irrotational at every instant. But the particle's deformation history — the accumulated strain from its journey through spatially varying gradients — creates a geometric memory that the instantaneous field doesn't possess. The irreversibility lives in the geometry of the trajectory, not in the dynamics of the flow.
This is the fluid-mechanical analog of Berry's phase in quantum mechanics: a system traverses a closed loop in parameter space and returns changed, not because of any force applied along the way, but because the space itself is curved. The predictions match experiments without fitting parameters — the geometry does the work.
Kassmi, 2603.24455. Fluid dynamics / geometric phase / transport / holonomy.