Constituent-Tagged Transfer Linking Cluster Dynamics to Static Scaling

Kenji Shinoda

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arXiv · 2609.02960

Constituent-Tagged Transfer Linking Cluster Dynamics to Static Scaling

Kenji Shinoda

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Abstract

Clusters that merge and split have no unique genealogy. Tracking the host size of a conserved constituent defines $q_*$ by $\langle(S_{t+\tau}/S_t)^{q_*}\rangle=1$, with $q_*\ne0$. Across coupled map networks, coagulation-fragmentation dynamics, and Vicsek systems, $q_*\simeq\alpha-2$ without fitting, where $c(s)\propto s^{-\alpha}$ on the same size window. Radius scans locate the known Vicsek interaction radius and recover an independently specified clustering scale in experimental active rods. Local scale covariance yields the relation, while a tent map counterexample shows when reducing the stationary balance at each parent size to one moment fails.

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Kenji Shinoda. 2026-09-02. Constituent-Tagged Transfer Linking Cluster Dynamics to Static Scaling. https://arxiv.org/abs/2609.02960

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