 Asymmetric simple exclusion process

The asymmetric simple exclusion process permits at most one particle per lattice site and biases jumps in one direction. A mean-field hydrodynamic limit has advective flux proportional to $c(1-c)$ because both an occupied departure site and vacant arrival site are required.

The Asymmetric Simple Exclusion Process (ASEP) is a stochastic mathematical model used to study the dynamics of particles (often thought of as simple "walkers") on a one-dimensional lattice. It is especially notable in the fields of statistical mechanics, condensed matter physics, and nonequilibrium statistical physics.