  We introduce a lattice gas model of cluster growth via the diffusive
aggregation of particles in a closed system obeying a local, deterministic,
microscopically reversible dynamics. This model roughly corresponds to placing
the irreversible Diffusion Limited Aggregation model (DLA) in contact with a
heat bath. Particles release latent heat when aggregating, while singly
connected cluster members can absorb heat and evaporate. The heat bath is
initially empty, hence we observe the flow of entropy from the aggregating gas
of particles into the heat bath, which is being populated by diffusing heat
tokens. Before the population of the heat bath stabilizes, the cluster
morphology (quantified by the fractal dimension) is similar to a standard DLA
cluster. The cluster then gradually anneals, becoming more tenuous, until
reaching configurational equilibrium when the cluster morphology resembles a
quenched branched random polymer. As the microscopic dynamics is invertible, we
can reverse the evolution, observe the inverse flow of heat and entropy, and
recover the initial condition. This simple system provides an explicit example
of how macroscopic dissipation and self-organization can result from an
underlying microscopically reversible dynamics.
