Tiny particles defy action-reaction symmetry to stay in motion

Tiny particles defy action-reaction symmetry to stay in motion Swati Mestri Scientific Editor Robert Egan Senior Editor From schools of fish and flocks of birds to microscopic synthetic particles, many systems in nature and the laboratory consist of individual units or agents that move by consuming energy. These systems are known as active matter because their components continuously use energy to generate motion, either individually or through interactions with their environment. Inspired by such systems, researchers have become increasingly interested in nonreciprocal interactions, in which the influence one particle exerts on another is not equally returned. In other words, one particle can affect another more strongly than it is affected in return, effectively breaking action-reaction symmetry. This is surprising because, under Newton's third law, passive particles cannot continuously push one another in the same direction. In this system, however, nonequilibrium electrohydrodynamic flows allow one particle to effectively "chase" another, so activity emerges even though the particles themselves are not self-propelled. Such asymmetry can generate entirely new forms of collective motion and self-organization. However, experimental realizations have largely been limited to small particle clusters. A research team led by professor Yutaka Sumino and assistant professor Kiwamu Yoshii of the Department of Applied Physics, Faculty of Advanced Engineering, Tokyo University of Science, Japan, has demonstrated large-scale collective dynamics driven by nonreciprocal interactions in a colloidal system containing more than 10,000 particles for more than 1 hour. An electric-field test bed The study, published in Physical Review Letters on Aug. 6, 2026, was conducted with Shoma Hara, a second-year master's student who completed the master's program in 2025; Keisuke Kittaka (2021); Hiroaki Ishikawa (2020); and Masazumi Okada (2019). "Our system provides an experimentally controllable example of nonreciprocal many-body physics, where broken action-reaction symmetry gives rise to collective phenomena," Sumino says. To create a system with nonreciprocal interactions, the researchers suspended polystyrene colloidal particles with radii of 1 and 1.5 micrometers in water and confined them between transparent indium-tin oxide-coated electrodes. When an alternating electric field was applied, electrohydrodynamic (EHD) flows developed around the particles. Because the strength of these flows increased strongly with particle size, larger particles generated stronger EHD flows than smaller particles. As a result, the EHD-mediated attractive interactions became asymmetric, causing larger particles to attract smaller particles more strongly than vice versa. This imbalance broke action-reaction symmetry and gave rise to nonreciprocal interactions. Pairs that move, clusters that split The experiments revealed that particles of different sizes spontaneously paired to form asymmetric structures with a distinct front and back. These pairs behaved as self-propelled units, moving through the suspension even though individual particles could not propel themselves. As more self-propelled pairs formed, they assembled into larger clusters. However, these clusters did not continue growing into giant aggregates. Instead, they repeatedly fragmented, rearranged and reformed. In contrast, suspensions containing particles of only one size exhibited reciprocal interactions and gradually formed static crystalline aggregates. The researchers note that similar nonreciprocal interactions are thought to occur in biological systems such as cell colonies and animal groups, suggesting that the mechanism identified here could provide a useful framework for understanding collective behavior in living systems. The researchers also reproduced the experimental observations using numerical simulations, which showed that nonreciprocal pair propulsion is the minimal mechanism required to generate persistent cluster dynamics. Because these ingredients are not unique to colloidal suspensions, the researchers expect similar behavior to emerge in a broad range of nonequilibrium systems. "This study demonstrates that the breaking of action-reaction symmetry can be a universal mechanism for matter to spontaneously form dynamic order. To put it more simply, particles that attract each other, such as sand, powder or raindrops, generally continue to gather over time, growing into larger clumps. However, in this study, we discovered that colloidal particles under an electric field exhibit unexpected behavior: They attract each other but do not form huge clumps, instead gathering and then splitting," Sumino explains. A broader route to dynamic order The researchers found that self-propelled particle pairs continuously generated motion within the clusters, preventing them from growing into giant aggregates. The findings show that nonreciprocal interactions can fundamentally alter conventional collective dynamics. Importantly, the system provides an experimentally controllable platform for studying nonreciprocal interactions in large particle assemblies and how they shape collective behavior. Although the work is primarily a fundamental study of nonequilibrium physics, the underlying design principle could eventually inspire programmable materials and externally controlled microrobotic systems, where groups of small agents assemble and reorganize collectively under external fields. "This research demonstrates that the breaking of action-reaction symmetry is a fundamental principle that generates new collective motions and self-organization of matter," Sumino says. These results further advance our understanding of the role that nonreciprocal interactions play in shaping collective dynamics. Publication details Shoma Hara et al, Arrested Coarsening in Active Colloidal Suspensions Driven by Nonreciprocal Electrohydrodynamic Interactions, Physical Review Letters (2026). DOI: 10.1103/96ky-d1p9. On arXiv: arxiv.org/abs/2509.23164 Journal information: Physical Review Letters , arXiv Key concepts Interactions in fluidsSelf-assemblyColloidsTheories of collective dynamics & active matterProvided by Tokyo University of Science