# Superadiabatic demixing in nonequilibrium colloids

T. Geigenfeind D. de las Heras, and M. Schmidt

Comms. Phys., **3**, 23, (2020) DOI: 10.1038/s42005-020-0287-5

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**Abstract**:

Dispersed colloidal particles that are set into systematic motion by a controlled external field constitute excellent model systems for studying structure formation far from equilibrium. Here we identify a unique demixing force that arises from repulsive interparticle interactions in driven binary colloids. The corresponding demixing force density is resolved in space and in time and it counteracts diffusive currents which arise due to gradients of the local mixing entropy. We construct a power functional approximation for overdamped Brownian dynamics that describes superadiabatic demixing as an antagonist to adiabatic mixing as originates from the free energy. We apply the theory to colloidal lane formation. The theoretical results are in excellent agreement with our Brownian dynamics computer simulation results for adiabatic, structural, drag and viscous forces. Superadiabatic demixing allows to rationalize the emergence of mixed, laned and jammed states in the system.

**Additional material/comments**:

Similar things tend to mix well. It takes differences in shape, size, or constitutive material in order to induce spatial segregation between constituents, which is often desired as in, say, the process of sorting similar things. Microscopically, this applies to atoms, molecules and mesoscopic colloidal particles. However, similar and even identical things can also segregate based on differences of their motion alone, as induced e.g. under gravity where inside of a liquid light particles cream up and heavy particles sediment down. Although in space, with no gravity, a perfectly homogeneous systems results. On earth however, the system separates top-bottom into compartments of either species.

We develop a theoretical treatment from first principles of driven Brownian multi-component systems. For the case of binary mixtures, the two components repel each other by a genuine nonequilibrium force, which we identify and model theoretically with a simple analytical expression for a generating mathematical object, the so-called superadiabatic excess free power functional. This object was proven to exist and be unique. The present contribution sheds much light on the structure and function of this complex mathematical entity. Our study hence paves the way for a systematic and detailed understanding of statistical physics of driven many-body systems.

We apply the theory to the relevant case of lane formation (segregation of two oppositely driven species into lanes). Lane formation is prototypical and transcends soft matter physics, as the effect is observed in countermoving groups of pedestrians, ants, etc. Colloidal physics provide a test bed for such general phenomena, where quantitative and predictive theories can be developed. As the power functional concept is general and its variants also apply to Molecular Dynamics and quantum dynamics, the present study forms a blueprint for the development of a unifying theoretical approach to many-body physics in nonequilibrium.

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