Corruption as a self-sustained collective state in political systems

Political corruption is often interpreted as the result of individual misconduct or isolated institutional failures.

However, persistent corruption patterns observed in real-world political systems suggest that systemic corruption may instead emerge as a self-sustaining governance arrangement supported by reinforcing interaction structures.

In this work, we introduce a minimal compartmental model for the dynamics of systemic political corruption and the formation of corruption-supporting relational structures.

The concentration of political power is treated as an emergent macroscopic observable arising from these coupled dynamics.

Despite its simplicity and mean-field character, the model exhibits a nontrivial phase transition separating regimes of low corruption from structurally captured states sustained by self-reinforcing interaction mechanisms.

The model predicts that, above a critical interaction strength, the captured state becomes dynamically stable, with small perturbations of the macroscopic variables naturally relaxing back to the stationary state.

We argue that this mechanism provides a possible explanation for the persistence of corruption across successive electoral cycles and institutional crises.

In particular, the political dynamics observed in the state of Rio de Janeiro, Brazil, provide a qualitative illustrative example of several mechanisms discussed by the proposed framework rather than a quantitative application of the model.

More broadly, the results suggest that long-term political capture may emerge spontaneously from reinforcing interactions between systemic corruption and the relational structures that sustain it, without requiring centralized coordination or complex strategic behavior.