Discovering state transitions in nonreciprocal living matter using topological flowscapes

Nonreciprocal interactions, in which action-reaction symmetry is broken, are abundant in nonequilibrium systems. However, their contribution to structural transitions in active and living matter remains to be seen. Here, we develop a living, nonreciprocal system with tunable interactions using a mixture of starfish embryos at different developmental stages. Through experiments, interaction inference and modeling, and analysis of local network topologies, we uncover a state diagram that comprises crystalline, flocking, and fragmented states. To uncover transitions between these states, we develop topological landscapes that map differences between distributions of structural motifs in their native metric space. Tuning the level of nonreciprocity, we find that weak asymmetric interactions enhance structural order, while higher nonreciprocity destabilizes it. Further, we develop a low-dimensional representation, a topological flowscape, to quantitatively compare transition pathways, revealing an information-rate shift for the state transition observed in our experiment. The topological flowscape framework presents a generalized method for nonequilibrium state transition detection and analysis, revealing the role of asymmetric interactions in the interplay of structure and dynamics of active matter.