Birds in flocks, bacteria, cells: in many collective systems, individual elements respond to only part of their surroundings, seemingly defying Newton’s third law of motion, that action equals reaction. These exceptions are known as non-reciprocal interactions. Even though these interactions do not stem from a potential, researchers at the Max Planck Institute for the Physics of Complex Systems have now developed a way to capture them in a Hamiltonian. The trick that made this possible is to introduce a fictitious partner for each component of the system to replace non-reciprocal interactions with reciprocal interactions with auxiliary degrees of freedom. This work advances the study of non-reciprocal systems significantly, because it enables use the established theoretical frameworks of many-body physics to describe these systems, which is an important step towards building the statistical mechanics of non-reciprocal systems.
Yu-Bo Shi, Roderich Moessner, Ricard Alert, and Marín Bukov, Nat. Phys. (2026)
Image credit: Kilian Neddermeyer
This highlight is based, in part, on the text of a press release by the ctd.qmat Cluster of Excellence (Universität Würzburg and TU Dresden), which is available here.