The asymmetric simple exclusion process is a toy model for describing nonequilibrium behavior. (Top) The model in the abstract. In an infinitesimal time window, a particle located on any one site hops to a site to its right with rate p, and to its left with rate q, provided these sites are empty. The lattice can exchange particles with the outside world, with particles entering or leaving the left end of the chain with rates α and γ, respectively, and entering and leaving the right side of the chain with rates δ and β, respectively. (Bottom) The model can be used to study protein “traffic” along a filament. In the case shown here, q, γ and δ are equal to zero.