Memory-Induced Curvature Drives Irreversible Transport in Irrotational Flows

Mounir Kassmi

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arXiv · 2604.08599

Memory-Induced Curvature Drives Irreversible Transport in Irrotational Flows

Mounir Kassmi

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Abstract

Irreversible transport in time-periodic flows is commonly attributed to vorticity, nonlinear forcing, or symmetry breaking. We show that finite-memory reconstruction of the velocity gradient generates a purely geometric mechanism for transport even when the instantaneous flow remains locally irrotational at all times. Memory promotes the velocity gradient to a history-dependent connection along particle trajectories whose noncommutativity produces a finite curvature over one forcing cycle. The associated holonomy generates a measurable loop displacement controlled solely by the dimensionless parameter {\omega}{\tau}_m, which quantifies the phase mismatch between forcing and reconstruction. The predicted scaling is consistent with independently reported measurements across distinct oscillatory flow configurations, supporting the interpretation of memory-induced curvature as a minimal geometric origin of irreversible transport in periodically driven continua.

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Mounir Kassmi. 2026-04-07. Memory-Induced Curvature Drives Irreversible Transport in Irrotational Flows. https://arxiv.org/abs/2604.08599

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