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Hidden nonreciprocity as a stabilizing effective potential in active matter

Matthew Du1,2,*, Andriy Goychuk3,†, and Suriyanarayanan Vaikuntanathan1,2,‡

  • *Contact author: madu@uchicago.edu
  • †Present address: Department of Systems Immunology, Helmholtz Centre for Infection Research, 38124 Braunschweig, Germany; Lower Saxony Center for Artificial Intelligence and Causal Methods in Medicine (CAIMed), Hannover, Germany; and Institute for Biochemistry, Biotechnology and Bioinformatics, Technische Universität Braunschweig, Braunschweig, Germany.
  • ‡Contact author: svaikunt@uchicago.edu
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Phys. Rev. Research 8, 033330 – Published 17 September, 2026

DOI: https://doi.org/10.1103/23zn-lzx2

Abstract

Nonreciprocal interactions are known to produce distinctive dynamics in active matter. To shed light on how the stationary state of such systems is affected by breaking reciprocity, we consider interacting particles propelled by persistent noise, where reciprocity is broken by a transverse force perpendicular to the gradient of the interaction energy. Focusing on the steady-state distribution of positions, we show that the nonreciprocal coupling helps keep the system at its stable configurations. Specifically, we demonstrate this effect for a variety of active systems whose stable configurations are energy minima, finding that the nonreciprocal coupling stiffens springs, aligns spins, and improves associative memory. In contrast, the transverse force does not change the stationary distribution of positions at all when the noise is thermal. Preliminary simulations suggest that this nonreciprocal coupling plays a similar stabilizing role in other active systems, such as those exhibiting motility-induced phase separation, whose stable configurations are not energy minima.

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Phys. Rev. Research 8, 033330– Published 17 September, 2026
  • Received 11 April 2024
  • Revised 25 February 2025
  • Accepted 5 August 2026
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