Geometric Memory Generates Irreversible Transport in Time-Periodic Irrotational Flows

Irreversible transport is generally attributed to vorticity, nonlinear forcing, or explicit symmetry breaking. We show that it can arise even in strictly time-periodic and locally irrotational flows through a purely geometric mechanism. By reconstructing the velocity gradient through causal self-transport over a finite memory time, deformation acquires the structure of a geometric connection whose holonomy generates a finite Lagrangian drift over one forcing cycle. The resulting contribution admits a closed-form, parameter-free expression. A quantitative consistency analysis using independently published experimental measurements shows that the predicted scaling and magnitude agree with observations without fitting or normalization. These results identify geometric memory as a minimal and generic source of irreversible transport.