  We study the early time and coarsening dynamics in the Light-Heavy model, a
system consisting of two species of particles ($light$ and $heavy$) coupled to
a fluctuating surface (described by tilt fields). The dynamics of particles and
tilts are coupled through local update rules, and are known to lead to
different ordered and disordered steady state phases depending on the
microscopic rates. We introduce a generalized balance mechanism in
non-equilibrium systems, namely $bunchwise~balance$, in which incoming and
outgoing transition currents are balanced between groups of configurations.
This allows us to exactly determine the steady state in a subspace of the phase
diagram of this model. We introduce the concept of $irreducible~sequences$ of
interfaces and bends in this model. These sequences are non-local, and we show
that they provide a coarsening length scale in the ordered phases at late
times. Finally, we propose a $local$ correlation function ($\mathcal{S}$) that
has a direct relation to the number of irreducible sequences, and is able to
distinguish between several phases of this system through its coarsening
properties. Starting from a totally disordered initial configuration,
$\mathcal{S}$ displays an initial linear rise and a broad maximum. As the
system evolves towards the ordered steady states, $\mathcal{S}$ further
exhibits power law decays at late times that encode coarsening properties of
the approach to the ordered phases. Focusing on early time dynamics, we posit
coupled mean-field evolution equations governing the particles and tilts, which
at short times are well approximated by a set of linearized equations, which we
solve analytically. Beyond a timescale set by a lattice cutoff and preceding
the onset of coarsening, our linearized theory predicts the existence of an
intermediate power-law stretch, which we also find in simulations of the
ordered regime of the system.
