Information-Optimal Mixing at Low Reynolds Number

Area of Science:

• Physics
• Statistical Mechanics
• Fluid Dynamics

Background:

• Mixing efficiency is crucial in microfluidics and soft matter.
• Low Reynolds number flows are governed by Stokes equation, exhibiting kinematic reversibility.
• Quantifying mixing efficiency often requires assumptions or specific system knowledge.

Purpose of the Study:

• To introduce a universal, assumption-free measure of mixing efficiency.
• To determine optimal control protocols for mixing in planar shear flows.
• To establish the minimum energetic cost of information erasure in nonequilibrium systems.

Main Methods:

• Utilizing mutual information between particle positions before and after mixing.
• Deriving a compact expression for mutual information as a functional of the shearing protocol.
• Solving the extremization problem for optimal control under shear and dissipation constraints.

Main Results:

• Mutual information provides a universal measure of mixing efficiency, accounting for Stokes equation reversibility.
• Optimal mixing protocols are derived and found to be universal and time-reversal symmetric.
• A minimum energetic cost for information erasure in drift-diffusive systems is established.

Conclusions:

• Mutual information is a powerful tool for quantifying mixing in low Reynolds number flows.
• Optimal mixing strategies are inherently time-reversal symmetric and universal.
• This work provides fundamental insights into the thermodynamics of information in nonequilibrium systems.