Self-propelled particles spontaneously cluster without attractive forces
Motility-induced phase separation (MIPS) occurs in run-and-tumble bacteria and active Brownian particles. Fast particles accumulate in dense regions because crowding slows them down, creating positive feedback. The instability occurs when the effective diffusivity d(rho*v)/d(rho) becomes negative — a purely non-equilibrium phase transition with no equilibrium analog.