Information-optimal mixing at low Reynolds number
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915349686910976 |
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| author | Cocconi, Luca Shi, Yihong Vilfan, Andrej |
| author_facet | Cocconi, Luca Shi, Yihong Vilfan, Andrej |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03567 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information-optimal mixing at low Reynolds number Cocconi, Luca Shi, Yihong Vilfan, Andrej Statistical Mechanics Fluid Dynamics 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. |
| title | Information-optimal mixing at low Reynolds number |
| topic | Statistical Mechanics Fluid Dynamics |
| url | https://arxiv.org/abs/2502.03567 |