Topological flowscape reveals state transitions in nonreciprocal living matter

TL;DR

This paper uncovers how asymmetric, nonreciprocal interactions influence structural state transitions in living systems, using starfish embryos to demonstrate a topological framework that maps and quantifies these nonequilibrium dynamics.

Contribution

It introduces topological landscapes and flowscapes as novel tools to analyze and understand state transitions driven by nonreciprocal interactions in active matter.

Findings

Weak nonreciprocity promotes structural order.

Stronger asymmetry disrupts ordered states.

Topological flowscapes quantify state transitions.

Abstract

Nonreciprocal interactions-- where forces between entities are asymmetric-- govern a wide range of nonequilibrium phenomena, yet their role in structural transitions in living and active systems remains elusive. Here, we demonstrate a transition between nonreciprocal states using starfish embryos at different stages of development, where interactions are inherently asymmetric and tunable. Experiments, interaction inference, and topological analysis yield a nonreciprocal state diagram spanning crystalline, flocking, and fragmented states, revealing that weak nonreciprocity promotes structural order while stronger asymmetry disrupts it. To capture these transitions, we introduce topological landscapes, mapping the distribution of structural motifs across state space. We further develop topological flowscapes, a dynamic framework that quantifies transitions between collective states and detects an informational rate shift from the experimental state transition. Together, these results establish a general approach for decoding nonequilibrium transitions and uncover how asymmetric interactions sculpt the dynamical and structural architecture of active and living matter.