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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

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

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

Nonreciprocity can profoundly alter the spectra and dynamics of open quantum systems, yet its impact on the long-time steady-state phases of matter has remained largely unexplored. Here we show that the interplay of nonreciprocity, symmetry…

Quantum Physics · Physics 2026-05-04 Ding Gu , Zhanpeng Fu , Zhong Wang

Nonreciprocal interactions violating Newton's third law are common in a plethora of nonequilibrium situations ranging from predator-prey systems to the swarming of birds and effective colloidal interactions under flow. While many recent…

Soft Condensed Matter · Physics 2025-10-07 Zhi-Feng Huang , Michael te Vrugt , Jonas Mayer Martins , Raphael Wittkowski , Hartmut Löwen

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

Non-reciprocal interactions between scalar fields that represent the concentrations of two active species are known to break the parity and time-reversal (PT) symmetries of the equilibrium state, as manifested in the emergence of travelling…

Statistical Mechanics · Physics 2022-09-01 Suropriya Saha , Ramin Golestanian

We investigate the transport properties of active particles undergoing a three-state run-and-tumble dynamics in one dimension, induced by non-reciprocal transition rates between self-propelling velocity states $\{-v, 0, +v\}$ that…

Statistical Mechanics · Physics 2025-08-15 Julio C. R. Romo-Cruz , Francisco J. Sevilla

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

The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…

Soft Condensed Matter · Physics 2024-06-03 Adam Wysocki , Roland G. Winkler , Gerhard Gompper

Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…

Statistical Mechanics · Physics 2024-12-06 Sergei Shmakov , Glasha Osipycheva , Peter B. Littlewood

In active matter, the lack of momentum conservation makes non-reciprocal interactions the rule rather than the exception. They lead to a rich set of emerging behaviors that are hard to account for and to predict starting from the…

Statistical Mechanics · Physics 2024-02-06 Alberto Dinelli , Jérémy O'Byrne , Agnese Curatolo , Yongfeng Zhao , Peter Sollich , Julien Tailleur

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

Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…

Statistical Mechanics · Physics 2025-04-01 Yael Avni , Michel Fruchart , David Martin , Daniel Seara , Vincenzo Vitelli

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

Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species…

Statistical Mechanics · Physics 2026-05-11 Arjun R , Pratyush Prakash Patra , A. V. Anil Kumar

We consider a generic system operating under non-equilibrium conditions. Explicitly, we consider an inertial classical Brownian particle dwelling a periodic structure with a spatially broken reflection symmetry. The particle is coupled to a…

Statistical Mechanics · Physics 2020-07-15 P. Hänggi , J. Łuczka , J. Spiechowicz

Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio=reactio on coarse-grained length and time scales.…

Soft Condensed Matter · Physics 2016-01-20 Jörg Bartnick , Marco Heinen , Alexei V Ivlev , Hartmut Löwen

We numerically investigate the phase separation dynamics of the non-reciprocal Allen-Cahn model in which two non-conserved order parameters are coupled. The system exhibits several dynamical patterns such as the randomly oscillating phase…

Soft Condensed Matter · Physics 2023-08-04 Maoji Liu , Zhanglin Hou , Hiroyuki Kitahata , Linli He , Shigeyuki Komura

Interactions between active particles may be non-reciprocal, breaking action-reaction symmetry and leading to novel physics not observed in equilibrium systems. The non-reciprocalCahn-Hilliard (NRCH) model is a phenomenological model that…

Soft Condensed Matter · Physics 2025-12-25 Martin Kjøllesdal Johnsrud , Ramin Golestanian
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