Chapter Three - Particle-Hopping Models of Transport Far from Equilibrium

Abstract

This chapter considers models obeying an exclusion principle such that each site can be occupied by at most one particle, and those without exclusion, where each site can be occupied by an arbitrary number of particles, but with particle conservation. From discrete mass transport models, it is only a small step to continuous mass transport models, often referred to as mass transfer models. Here, discrete particles re not distinguished, but the dynamical variable at each lattice site is interpreted as a continuous mass. The elementary dynamical step then consists of moving a certain fraction of this mass to a neighboring site. Mass is determined by some prescribed probability density. Particle-hopping models conserve the particle number in the bulk in the case of nearest-neighbor interactions. This conservation law implies that particles are transported in the system through hopping to neighbor sites. In general, this transport will be asymmetric in the sense that rates for motion to the left and right are different. If the particles have an internal degree of freedom, corresponding to a multistate model, only the total number of particles needs to be conserved, not that of each species separately.