  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.
