Explicit Calculations on Small Non-Equilibrium Driven Lattice Gas Models

We have investigated the non-equilibrium nature of a lattice gas system consisting of a regular lattice of charged particles driven by an external electric field. For a big system, an exact solution cannot be obtained using a master equation approach since the many-particle system has too many degrees of freedom to allow for exact solutions. We have instead chosen to study small systems as a first step. The small systems will be composed of between two and four particles having two or three possible values of some parameters. Applying periodic boundary conditions and a hard-core or an exclusion-volume constraint and imposing conservation of particle numbers via Kawasaki-type dynamics (particle-hole exchange), we are able to calculate the exact solutions of the steady-state relative probability density function, ri, associated with each configuration of the small system.