  Consider a one-dimensional exclusion process with finite-range
translation-invariant jump rates with non-zero drift. Let the process be
stationary with product Bernoulli invariant distribution at density \rho. Place
a second class particle initially at the origin. For the case \rho different
from 1/2 we show that the time spent by the second class particle at the origin
has finite expectation. This strong transience is then used to prove that
variances of additive functionals of local mean-zero functions are diffusive
when \rho is not 1/2. As a corollary to previous work, we deduce the invariance
principle for these functionals. The main arguments are comparisons of H_{-1}
norms, a large deviation estimate for second-class particles, and a relation
between occupation times of second-class particles and additive functional
variances.
