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Liquid Hopfield model: retrieval and localization in multicomponent liquid mixtures
Biological Physics · Submitted 28 Oct 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Taken together, our results demonstrate a trade-off between retrieval and localization phenomena in liquid mixtures.
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The abstract, sentence by sentence
Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. These structures compete with each other for the same components. This raises several questions, such as what types of interactions allow the retrieval of multiple ordered mesoscopic structures, and what are the physical limitations for the retrieval of said structures. In this work, we develop an analytically tractable model for liquids capable of retrieving states with target compositions. We name this model the liquid Hopfield model in reference to corresponding work in the theory of associative neural networks. By solving this model, we show that non-linear repulsive interactions are necessary for retrieval of target structures. We demonstrate that this is because liquid mixtures at low temperatures tend to transition to phases with few components, a phenomenon that we term localization. Taken together, our results demonstrate a trade-off between retrieval and localization phenomena in liquid mixtures.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. | background 1.00 | 0.04 | 0.01 | asserted 1.00 |
| s1 | From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. | background 1.00 | 0.08 | 0.03 | asserted 1.00 |
| s2 | These structures compete with each other for the same components. | background 0.98 | 0.07 | 0.03 | asserted 1.00 |
| s3 | This raises several questions, such as what types of interactions allow the retrieval of multiple ordered mesoscopic structures, and what are the physical limitations for the retrieval of said structures. | gap 0.88 | 0.04 | 0.03 | unclear 0.80 |
| s4 | In this work, we develop an analytically tractable model for liquids capable of retrieving states with target compositions. | contribution 0.75 | 0.96 | 0.06 | asserted 0.99 |
| s5 | We name this model the liquid Hopfield model in reference to corresponding work in the theory of associative neural networks. | contribution 0.57 | 0.77 | 0.03 | asserted 0.98 |
| s6 | By solving this model, we show that non-linear repulsive interactions are necessary for retrieval of target structures. | result 1.00 | 0.95 | 0.42 | asserted 1.00 |
| s7 | We demonstrate that this is because liquid mixtures at low temperatures tend to transition to phases with few components, a phenomenon that we term localization. | interpretation 0.75 | 0.90 | 0.20 | asserted 1.00 |
| s8 | Taken together, our results demonstrate a trade-off between retrieval and localization phenomena in liquid mixtures. | interpretation 0.84 | 0.93 | 0.87 | asserted 1.00 |
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The paper
Original abstract
Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. These structures compete with each other for the same components. This raises several questions, such as what types of interactions allow the retrieval of multiple ordered mesoscopic structures, and what are the physical limitations for the retrieval of said structures. In this work, we develop an analytically tractable model for liquids capable of retrieving states with target compositions. We name this model the liquid Hopfield model in reference to corresponding work in the theory of associative neural networks. By solving this model, we show that non-linear repulsive interactions are necessary for retrieval of target structures. We demonstrate that this is because liquid mixtures at low temperatures tend to transition to phases with few components, a phenomenon that we term localization. Taken together, our results demonstrate a trade-off between retrieval and localization phenomena in liquid mixtures.
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3 arXiv papers cite this in 3 sentences
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Cites it as background 2 papers
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We here also focused on interactions that are randomly distributed with little structure, whereas realistic systems will likely have higher-order [ref] and structured interactions [ref] , e.g., arising from evolutionary optimization, which affects phase separation [ref] .
Generic multicomponent mixtures are multistable · Discussion · 0.85
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This effectively turns the tile pool into an associative memory, reminiscent of a Hopfield network [ref] .
Escaping kinetic traps using non-reciprocal interactions · Introduction · 0.88
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