  This is the second in a series of three papers in which we study a lattice
gas subject to Kawasaki conservative dynamics at inverse temperature $\beta>0$
in a large finite box $\Lambda_\beta \subset\mathbb Z^2$ whose volume depends
on $\beta$. Each pair of neighbouring particles has a negative binding energy
$-U<0$, while each particle has a positive activation energy $\Delta>0$. The
initial configuration is drawn from the grand-canonical ensemble restricted to
the set of configurations where all the droplets are subcritical. Our goal is
to describe, in the metastable regime $\Delta\in(U,2U)$ and in the limit as
$\beta\to\infty$, how and when the system nucleates.
  In the first paper we showed that subcritical droplets behave as quasi-random
walks. In the present paper we use the results in the first paper to analyse
how subcritical droplets form and dissolve on multiple space-time scales when
the volume is moderately large, i.e., $|\Lambda_\beta|=\mathrm e^{\Theta\beta}$
with $\Delta<\Theta<2\Delta-U$. In the third paper we consider the setting
where the volume is very large, namely, $|\Lambda_\beta|=\mathrm
e^{\Theta\beta}$ with $\Delta<\Theta<\Gamma-(2\Delta-U)$, where $\Gamma$ is the
energy of the critical droplet in the local model with fixed volume, and use
the results in the first two papers to identify the nucleation time. We will
see that in a very large volume critical droplets appear more or less
independently in boxes of moderate volume, a phenomenon referred to as
homogeneous nucleation.
  Since Kawasaki dynamics is conservative, i.e., particles are preserved, we
need to control non-local effects in the way droplets are formed and dissolved.
This is done via a deductive approach: the tube of typical trajectories leading
to nucleation is described via a series of events on which the evolution of the
gas consists of droplets wandering around on multiple space-time scales.
