Mémoire

Abstract

Classical mechanics rests on the reciprocity of interactions, as encapsulated in Newton's third law and formalized through Noether’s theorem, which links continuous symmetries to conservation laws. Yet, many physical systems of current interest, from biological collectives to synthetic active matter, violate these assumptions and operate beyond the scope of the traditional variational framework.

In this work, we investigate how breaking reciprocity modifies the structural and dynamical organization of a two-species particle system. Using a discrete element method (DEM) simulation, particles interact through type-dependent forces encoded in an interaction matrix, with a control parameter interpolating between fully reciprocal and maximally non-reciprocal regimes.

Our results reveal a transition from momentum-conserving assemblies to self-organized, motile clusters as reciprocity is broken. Reciprocal interactions yield static or weakly fluctuating structures, while non-reciprocal couplings generate persistent motion, coherent patterns, and core-shell cluster morphologies. The onset of these behaviors depends sensitively on the interaction range and population ratio of the two species. Furthermore, the loss of momentum conservation is linked to the breakdown of Noether’s theorem, establishing a conceptual bridge between microscopic asymmetry and emergent collective motion.

This work highlights non-reciprocity as a fundamental physical mechanism for self-organization, offering a minimal framework to explore how microscopic asymmetries can give rise to macroscopic order.