TASEP: Totally Asymmetric Simple Exclusion Process

TASEP is a paradigmatic nonequilibrium model: particles enter with rate α, hop right with rate 1 (if empty), exit with rate β. Exact Bethe ansatz solution reveals three phases: Low Density (LD), High Density (HD), Maximum Current (MC), meeting at a triple point α=β=1/2. Current J = ρ(1-ρ) with max J=1/4.