Recent progress in non-equilibrium structure and dynamics of connected active agents.

Active agents, which convert energy into directed motion, are inherently non-equilibrium systems. Inspired by living organisms and polymer physics, connected active agents with various topologies have recently garnered significant attention. These agents have positional degrees of freedom with well-defined topologies, while activity introduces extra degrees of freedom. The intricate interplay of activity, elasticity, noise, and conformational degrees of freedom gives rise to novel non-equilibrium behaviors in chain-like structures. This review categorizes active agents into three types based on their alignment mechanisms: Active Brownian agents, Vicsek-type agents, and self-aligning agents. It further provides the results when these agents are connected through different topological structures in two-dimensional spaces, at interfaces, in three-dimensional environments, and under confinement. The goal is to shed light on the fundamental physics that govern their non-equilibrium behavior at the level of individual chains and to highlight potential research directions. These findings hold significant potential for advancing the design of metamaterials and swarm robotics.