From Active to Odd to Smart Matter

Abstract

The study of active matter has reshaped our understanding of collective states of matter far from equilibrium by proving that energy pumped into the microscopic scale leads to order on the macroscopic scale, collective motion, and anomalous mechanical responses. More recently, the discovery of odd elasticity and nonreciprocal mechanical couplings has extended these ideas to solid-like active systems, revealing materials with nonconservative elastic response. Simultaneously, innovative developments in swarm robotics , programmable metamaterials , and learning algorithms have led to the emergence of a new frontier in which collective behavior and mechanical response are no longer fixed by design, but adapted, optimized, and learned toward functional goals. This Perspective proposes a unifying trajectory, from active to odd to smart matter, organized along two intertwined axes: the traditional gas--liquid--solid progression of condensed matter, and the more recentparadigm shift from spontaneous collective dynamics to task-driven functionality. We try to highlight emerging principles, conceptual shifts, and open challenges that come along this trajectory, and argue that learning may play the role of a specific form of emergence, which could advantageously replace the more traditional view of control, at least in the realm of physics.