Chapter Four - Asymmetric Simple Exclusion Process – Exact Results

Abstract

One of the properties of asymmetric simple exclusion process (ASEP) is the fact that many exact results can be obtained. It is the simplest possible stochastic transport model and a genuine non equilibrium model, which belongs to the class of driven diffusive systems. This chapter sketches how these numerous exact results can be derived. At the same time, the application of several of the theoretical methods is demonstrated. Two different terminologies are commonly used in the literature. Totally asymmetric simple exclusion process (TASEP), in which motion is allowed only in one direction. The behavior of the partially asymmetric version (PASEP) is usually not very different. The chapter considers the simpler case of periodic boundary conditions that leads to a translational-invariant stationary state. Steady state is quite simple in random-sequential dynamics and parallel update is relevant for traffic models. The steady state is slightly more complicated. The unidirectional variant of the ASEP is referred to as TASEP. The variant, where hopping in both directions is allowed is either called ASEP or PASEP.