TASEP — Totally Asymmetric Simple Exclusion

Particles enter from left (rate α), hop right if the next site is empty, and exit right (rate β). Three phases emerge: low-density (α-limited), high-density (β-limited), and maximal-current. The kymograph shows space-time trajectories.

Phase diagram (α vs β)
Phase:
Current J:
Density ρ: