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The formation of dynamical patterns is one of the most striking features of nonequilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as nonreciprocal…

Statistical Mechanics · Physics 2025-08-26 James Mason , Robert L. Jack , Maria Bruna

Pair interactions between active particles need not follow Newton's third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical…

Statistical Mechanics · Physics 2020-10-21 Suropriya Saha , Jaime Agudo-Canalejo , Ramin Golestanian

Newton's third law, actio = reactio, is a foundational statement of classical mechanics. However, in natural and living systems, this law appears to be routinely violated for constituents interacting in a nonequilibrium environment. Here,…

Soft Condensed Matter · Physics 2023-05-30 Yu-Jen Chiu , Ahmad K. Omar

Nonreciprocity is known to generate a wide range of exotic phenomena in multi-species many-body systems, where different species influence one another through couplings that violate Newton's third law. In contrast, in the absence of…

Statistical Mechanics · Physics 2026-04-02 Wei-Chen Guo , Zuo Wang , Pei-Fang Wu , Li-Jun Lang , Bao-Quan Ai , Liang He

Nonreciprocal active matter systems typically feature an asymmetric role among interacting agents, such as a pursuer-evader relationship. We propose a multi-species nonreciprocal active matter model that is invariant under permutations of…

Statistical Mechanics · Physics 2025-12-23 Chul-Ung Woo , Heiko Rieger , Jae Dong Noh

We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations of the microscopic model and linear stability analysis of the associated coarse-grained field theory, we identify a…

Statistical Mechanics · Physics 2023-10-13 Yu Duan , Jaime Agudo-Canalejo , Ramin Golestanian , Benoît Mahault

Non-reciprocal interactions are among the simplest mechanisms that drive a physical system out of thermal equilibrium, leading to novel phenomena such as oscillatory pattern formation. In this paper, we introduce a ternary phase separation…

Soft Condensed Matter · Physics 2025-12-09 Xiao Ma , Michael E. Cates

Active particle systems of interacting self-propelled particles offer a versatile framework for modeling complex systems. When employed to describe aspects of animal behavior, the complexity of animal movement and decision-making often…

Biological Physics · Physics 2025-01-09 Amir Haluts , Dan Gorbonos , Nir S. Gov

Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave…

Soft Condensed Matter · Physics 2021-04-20 Michel Fruchart , Ryo Hanai , Peter B. Littlewood , Vincenzo Vitelli

Motility and nonreciprocity are two primary mechanisms for self-organization in active matter. In a recent study [Phys. Rev. Lett. 131, 148301 (2023)], we explored their joint influence in a minimal model of two-species quorum-sensing…

Soft Condensed Matter · Physics 2025-04-15 Yu Duan , Jaime Agudo-Canalejo , Ramin Golestanian , Benoît Mahault

Emergent non-reciprocal interactions violating Newton's third law are widespread in out-of-equilibrium systems. Phase separating mixtures with such interactions exhibit travelling states with no equilibrium counterpart. Using extensive…

Statistical Mechanics · Physics 2024-07-10 Rituparno Mandal , Santiago Salazar Jaramillo , Peter Sollich

Nonreciprocal interactions that violate Newton's law 'actio=reactio' are ubiquitous in nature and are currently intensively investigated in active matter, chemical reaction networks, population dynamics, and many other fields. An…

Statistical Mechanics · Physics 2026-02-24 Atul Tanaji Mohite , Heiko Rieger

We examine a non-reciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross diffusivities, provides a generic mechanism for the…

Soft Condensed Matter · Physics 2020-08-21 Zhihong You , Aparna Baskaran , M. Cristina Marchetti

In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We…

Pattern Formation and Solitons · Physics 2024-04-23 Fridtjof Brauns , M. Cristina Marchetti

The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents, and a key component in the structuring of many biological systems.The relationships between the ordering process and the underlying…

Soft Condensed Matter · Physics 2020-12-02 Jonas Denk , Erwin Frey

Pattern formation in active biological matter typically arises from the feedback between chemical concentration fields and mechanical stresses. The actomyosin cortex of cells is an archetypal example of an active thin film that displays…

Biological Physics · Physics 2025-10-17 Jason R. Picardo , V. Jemseena , K. Vijay Kumar

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

Adaptation and Self-Organizing Systems · Physics 2016-01-21 Nick McCullen , Thomas Wagenknecht

Two hallmarks of non-equilibrium systems, from active colloids to animal herds, are agents motility and nonreciprocal interactions. Their interplay creates feedback loops leading to complex spatiotemporal dynamics crucial to understand and…

Statistical Mechanics · Physics 2025-09-17 David Martin , Daniel Seara , Yael Avni , Michel Fruchart , Vincenzo Vitelli

We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links.…

Pattern Formation and Solitons · Physics 2025-10-22 Timoteo Carletti , Riccardo Muolo

Active agents are capable of exerting nonreciprocal forces upon one another. For instance, one agent, say $A$, may attract another agent $B$ while $B$ repels $A$. These antagonistic nonreciprocal interactions have been extensively studied…

Quantum Physics · Physics 2025-01-23 Tobias Nadolny , Christoph Bruder , Matteo Brunelli
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