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  • Open Access

Metastable Phase Separation and Information Retrieval in Multicomponent Liquids

Davide Marcato*

Rodrigo Braz Teixeira*

Izaak Neri‡

Pablo Sartori†

  • *These authors contributed equally to this work.
  • †Contact author: pablo.sartori@gimm.pt
  • ‡Contact author: izaak.neri@kcl.ac.uk
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Phys. Rev. X 16, 041033 – Published 5 November, 2026

DOI: https://doi.org/10.1103/lxrw-98f4

Abstract

Liquid mixtures can separate into phases with distinct composition. This phenomenon has recently come back to prominence due to its role in complex biological liquids, such as the cytoplasm, which contain thousands of components. For simple two-component mixtures phase-separated states are global free energy minima. However, local free energy minima, i.e., metastable states, are known to play a dominant role in complex systems with many components. For example, Hopfield neural networks can retrieve stored information from partial cues via relaxation to metastable states. Under what conditions can phase separated states be metastable, and what are the implications for information retrieval in multicomponent liquids? In this work we develop the general thermodynamic formalism of metastable phase separation. We then apply this formalism to an illustrative toy example inspired by recent experiments, binary mixtures with high-order interactions. Finally, as core application of the formalism, we study metastability in Hopfield liquids, a class of multicomponent mixtures capable of storing information on the composition of phases. We show that these phases can be nucleated from partial cues via metastable phase separation. Spatial simulations of liquids with a large number of components match our analytical solution. Our work suggests that complex biological mixtures can retrieve information through metastable phase separation.

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Popular Summary

Neural networks can recall memories from a partial cue. We show that liquid mixtures can do something similar. Inside cells, mixtures like the cytoplasm and nucleoplasm demix by liquid-liquid phase separation into membraneless compartments called biomolecular condensates, each built from its own particular mix of components. These condensates are thought to be metastable: not the most stable arrangement the mixture could reach, only a long-lived one. We develop a thermodynamic theory of when such metastable states exist, and find that many distinct compositions can be stored simultaneously. A small cluster containing only part of a target composition can seed a droplet that grows into the complete composition, recovering a stored pattern from an incomplete cue. This offers a new way to think about how cells assemble condensates of precise composition from a crowded molecular soup, and a design principle for synthetic mixtures that demix into phases of prescribed composition.

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Phys. Rev. X 16, 041033– Published 5 November, 2026
  • Received 26 September 2025
  • Revised 25 June 2026
  • Accepted 20 August 2026
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