  Steady state properties of hard objects with exclusion interaction and a
driven motion along a one-dimensional periodic lattice are investigated. The
process is a generalization of the asymmetric simple exclusion process (ASEP)
to particles of length k, and is called the k-ASEP. Here, we analyze both
static and dynamic properties of the k-ASEP. Density correlations are found to
display interesting features, such as pronounced oscillations in both space and
time, as a consequence of the extended length of the particles. At long times,
the density autocorrelation decays exponentially in time, except at a special
k-dependent density when it decays as a power law. In the limit of large k at a
finite density of occupied sites, the appropriately scaled system reduces to a
nonequilibrium generalization of the Tonks gas describing the motion of hard
rods along a continuous line. This allows us to obtain in a simple way the
known two-particle distribution for the Tonks gas. For large but finite k, we
also obtain the leading-order correction to the Tonks result.
