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 , and to its left with rate , 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 and , respectively, and entering and leaving the right side of the chain with rates and , respectively. (Bottom) The model can be used to study protein “traffic” along a filament. In the case shown here, , and are equal to zero.