A thermodynamically reversible generalization of Diffusion Limited Aggregation

TL;DR

This paper presents a reversible lattice gas model of cluster growth that mimics diffusion limited aggregation in contact with a heat bath, illustrating how macroscopic irreversibility emerges from microscopic reversibility.

Contribution

It introduces a reversible, thermodynamically consistent model of cluster growth, bridging microscopic reversibility with macroscopic dissipation and self-organization.

Findings

Cluster morphology initially resembles standard DLA.

Clusters become more tenuous and equilibrate over time.

The model demonstrates reversibility of the aggregation process.

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.