Information-Optimal Mixing at Low Reynolds Number

Mutual information between particle positions before and after mixing provides a universal assumption-free measure of mixing efficiency at low Reynolds number that 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 extremization problem exactly to determine the optimal control under both linear and nonlinear 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 nonequilibrium drift-diffusive systems.