  We study conservative particle systems on W^S, where S is countable and W =
{0, ..., N} or the natural numbers. The rate of a particle moving from site x
to site y is given by p(x,y) b(eta_x, eta_y), where eta_z is the number of
particles at site z. Under assumptions on b and the assumption that p is finite
range, which allow for the exclusion, zero range and misanthrope processes, we
show exactly what the stationary product measures are.
  Furthermore we show that a stationary measure mu is ergodic if and only if
the tail sigma algebra of the partial sums is trivial under mu. This is a
consequence of a more general result on interacting particle systems that shows
that a stationary measure is ergodic if and only if the sigma algebra of sets
invariant under the transformations of the process is trivial. We apply this
result combined with a coupling argument on the stationary product measures to
determine which product measures are ergodic. For the case that W is finite
this gives a complete characterisation.
  For the case that W is the set of natural numbers we show that for nearly all
functions b a stationary product measure is ergodic if and only if it is
supported by configurations with an infinite amount of particles. We show that
this picture is not complete, we give an example of a system where b is such
that there is a stationary product measure which is not ergodic, even though it
concentrates on configurations with an infinite number of particles.
