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.
The study, published in Physical Review Letters on August 6, 2026, was conducted together 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," says Prof. Sumino.
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.
The experiments revealed that particles of different sizes spontaneously paired together to form asymmetric structures with a distinct front and back. These pairs behaved as self-propelled units, moving through the suspension despite the fact that 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 behaviors 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," explains Prof. Sumino.
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," says Prof. Sumino.
These results further advance our understanding of the role that nonreciprocal interactions play in shaping collective dynamics.
Reference
Title of original paper: Arrested coarsening in active colloidal suspensions driven by nonreciprocal electrohydrodynamic interactions
Journal: Physical Review Letters
DOI: https://doi.org/10.1103/96ky-d1p9
About The Tokyo University of Science
Tokyo University of Science (TUS) is a well-known and respected university, and the largest science-specialized private research university in Japan, with four campuses in central Tokyo and its suburbs and in Hokkaido. Established in 1881, the university has continually contributed to Japan's development in science through inculcating the love for science in researchers, technicians, and educators.
With a mission of "Creating science and technology for the harmonious development of nature, human beings, and society," TUS has undertaken a wide range of research from basic to applied science. TUS has embraced a multidisciplinary approach to research and undertaken intensive study in some of today's most vital fields. TUS is a meritocracy where the best in science is recognized and nurtured. It is the only private university in Japan that has produced a Nobel Prize winner and the only private university in Asia to produce Nobel Prize winners within the natural sciences field.
Website: https://www.tus.ac.jp/en/mediarelations/
About Professor Yutaka Sumino from Tokyo University of Science
Professor Yutaka Sumino is a faculty member in the Department of Applied Physics, Faculty of Advanced Engineering, at Tokyo University of Science. He received his Doctor of Science degree from Kyoto University and leads the Artificial Life Physics (Sumino Lab). His research explores how life-like behaviors emerge from simple physical systems, with interests spanning nonequilibrium physics, biophysics, chemical physics, and collective dynamics. His work investigates self-organizing phenomena at mesoscopic interfaces, including pattern formation, collective motion, self-propelled droplets, colloidal systems, and microrobotics.
Funding information
The financial support was provided by the JSPS KAKENHI (grants numbers: JP16K13866, JP19H05403, JP21H01004, JP21H00409, JP24KJ0110, and JP26K07037), including the Grant-in-Aid for Transformative Research Areas (A), "Dynamic Materials Science: Quantum-inspired active matter and function designs" (grant numbers: JP26H00387); by the JSPS and PAN under the Japan-Poland Research Cooperative Program, "Spatio-temporal patterns of elements driven by self-generated, geometrically constrained flows;" and by the JSPS Core-to-Core Program, "Advanced core-to-core network for the physics of self-organizing active matter" (grant number: JPJSCCA20230002).
