Nonextensive Supercluster States in Aggregation with Fragmentation

Area of Science:

• Complex systems
• Statistical physics

Background:

• Systems evolving via aggregation and fragmentation can exhibit unique states.
• The supercluster state (SCS) is characterized by large clusters, resembling a gelling state.
• SCS formation is influenced by fluctuations, similar to critical phenomena.

Purpose of the Study:

• To investigate the properties of the supercluster state (SCS) in evolving systems.
• To differentiate the SCS from equilibrium and jamming states.
• To develop a theoretical framework for describing the SCS.

Main Methods:

• Proposed a scaling approach with critical exponents to characterize the SCS.
• Utilized theoretical analysis, noting the failure of conventional methods like van Kampen expansion.
• Validated theoretical findings with numerical simulations.

Main Results:

• The SCS is a nonextensive state where cluster number scales sublinearly with system size.
• The SCS occupies a distinct region in the parameter space, separating equilibrium and jamming (extensive) states.
• The proposed scaling approach successfully described the SCS.

Conclusions:

• The supercluster state (SCS) is a novel, non-gelling, non-jamming state in evolving systems.
• A scaling theory with critical exponents is effective for characterizing the SCS.
• The findings offer new insights into the behavior of complex systems near criticality.