Self-propelled particles, run-and-tumble dynamics, non-equilibrium coexistence without attraction
MIPS mechanism: slow particles → local density↑ → further slowdown → phase separation
Effective pressure: P(φ) = ρv₀²/(2λ) · (1-φ/φ_max)ʰ — non-monotonic → spinodal instability
MIPS is a hallmark of active matter: purely repulsive self-propelled particles phase-separate into dense (liquid) and dilute (gas) regions with NO attractive interactions. Mechanism: particles slow down in dense regions (here: excluded volume). Run-and-tumble persistence length ℓ=v₀/λ. MIPS onset: ℓ ≫ particle size and φ above spinodal. Unlike equilibrium Cahn-Hilliard, no detailed balance — effective temperature ill-defined.