First assembly times and equilibration in stochastic coagulation-fragmentation.

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Complex Systems

Background:

• Coagulation and fragmentation (CF) processes are fundamental in various scientific fields.
• Classical mass-action models often simplify these processes, potentially overlooking stochastic effects.
• Finite systems with size constraints introduce complexities not fully captured by traditional models.

Purpose of the Study:

• To develop a fully stochastic theory for CF in finite systems with a maximum cluster size.
• To derive analytical results for equilibrium cluster distributions and mean assembly times.
• To compare stochastic predictions with classical mass-action models.

Main Methods:

• Development of a high-dimensional master equation for cluster configurations.
• Exact analytical solutions for equilibrium cluster distributions under specific conditions.
• State-space enumeration to determine mean assembly times.

Main Results:

• A broader mean cluster-size distribution than predicted by mass-action models when coagulation dominates and system mass is indivisible by the maximum cluster size.
• Identification of conditions that accelerate equilibration and prevent late-stage coarsening.
• Derivation of scaling laws for mean assembly times, showing CF accelerates assembly only in specific cases.

Conclusions:

• Stochastic effects significantly influence cluster distributions and assembly dynamics in finite CF systems.
• Classical mass-action models can fail to accurately describe self-assembly under certain conditions.
• A high-dimensional discrete stochastic model is crucial for accurately capturing these phenomena.