Active Brownian particles — density-dependent speed drives phase coexistence
Motility-Induced Phase Separation (MIPS) occurs when self-propelled particles slow down in crowded regions. Slow particles accumulate further, creating a positive feedback that drives gas–liquid-like coexistence — purely from activity, with no attractions. The effective free energy has a spinodal instability at high v₀ and low Dr (long persistence length ℓ = v₀/Dr). This is a fundamentally non-equilibrium phenomenon with no equilibrium analogue.