Non-extensive super-cluster states in aggregation with fragmentation

TL;DR

This paper investigates a unique super-cluster state in systems with aggregation and fragmentation, characterized by non-extensiveness and critical-like fluctuations, and introduces a scaling approach to analyze it.

Contribution

It introduces a novel scaling method with critical exponents to describe the non-extensive super-cluster state in aggregation-fragmentation systems.

Findings

The super-cluster state is non-extensive and separates equilibrium and jamming states.

Conventional methods like van Kampen expansion fail to describe the SCS.

The proposed scaling approach aligns well with numerical simulations.

Abstract

Systems evolving through aggregation and fragmentation may possess an intriguing super-cluster state (SCS). Clusters constituting this state are mostly large, so the SCS resembles a gelling state. The formation of the SCS is controlled by fluctuations and in this aspect, it is similar to a critical state. The SCS is non-extensive as the number of clusters varies sub-linearly with the system size. In the parameter space, the SCS separates equilibrium and jamming (extensive) states. The conventional methods such as the van Kampen expansion fail to describe the SCS. To characterize the SCS, we propose a scaling approach with a set of critical exponents. Our theoretical findings are in good agreement with numerical results.