Information-optimal mixing at low Reynolds number

Luca Cocconi; Yihong Shi; Andrej Vilfan

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arXiv · 2502.03567

Information-optimal mixing at low Reynolds number

Luca Cocconi·Yihong Shi·Andrej Vilfan

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Abstract

Mutual information between particle positions before and after mixing provides a universal assumption-free measure of mixing efficiency at low Reynolds number which accounts for the kinematic reversibility of the Stokes equation. For a generic planar shear flow with time-dependent shear rate, we derive a compact expression for the mutual information as a nonlinear functional of the shearing protocol and solve the associated extremisation problem exactly to determine the optimal control under both linear and non-linear constraints, specifically total shear and total dissipation per unit volume. Remarkably, optimal protocols turn out to be universal and time-reversal symmetric in both cases. Our results establish a minimum energetic cost of erasing information in a broad class of non-equilibrium drift-diffusive systems.

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Luca Cocconi, Yihong Shi, Andrej Vilfan. 2025-02-05. Information-optimal mixing at low Reynolds number. https://arxiv.org/abs/2502.03567

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