Thermodynamically reversible generalization of diffusion limited aggregation

Abstract

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. We present a detailed description of the dynamics for the model, discuss the macroscopic limit, and give predictions for the equilibrium particle densities obtained in the mean field limit. Empirical results for the growth are then presented, including the observed equilibrium particle densities, the temperature of the system, the fractal dimension of the growth clusters, scaling behavior, finite size effects, and the approach to equilibrium. We pay particular attention to the temporal behavior of the growth process and show that the relaxation to the maximum entropy state is initially a rapid nonequilibrium process, then subsequently it is a quasistatic process with a well defined temperature.