A generic coupling between internal states and activity leads to activation fronts and criticality in active systems

To understand the onset of collective motion, we investigate active systems where particles switch on and off their self-propulsion. We prove that even when the only possible transition is off$\to$on, an active 2-state system behaves as an effective 3-state system that exhibits a sharp phase transition in 1D, and critical behavior in 2D, with scale-invariant activity avalanches. The obtained results show how criticality can naturally emerge in active systems, providing insight into the way collectives distribute, process, and respond to local environmental cues.