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arXiv · 2602.15256

Environment-Driven Emergence of Higher-Order Collective Behavior

Felipe S. Abril-Bermúdez·David N. Fisher·Jean-Baptiste Gramain·Francisco J. Pérez-Reche
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Abstract

Collective behavior is commonly attributed to direct interactions among system components. Using a minimal stochastic model, we show that higher-order collective structure can instead emerge from shared stochastic environments, even in the absence of interactions. Quantified via the O-information, environmental fluctuations induce both redundant and synergistic dependencies, with the latter occupying larger regions of the correlation space. We establish a no-go theorem showing that time-independent coupling between the system variables and a shared stochastic environment rules out synergistic higher-order behavior. Crucially, this constraint can be overcome dynamically: transitions between redundancy and synergy arise from time-dependent environmental coupling or from the nontrivial interplay between shared environments and direct interactions. Together, these results identify environmental mediation as a distinct mechanism of higher-order collective organization beyond the conventional interaction-centric paradigm.

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Felipe S. Abril-Bermúdez, David N. Fisher, Jean-Baptiste Gramain, Francisco J. Pérez-Reche. 2026-02-16. Environment-Driven Emergence of Higher-Order Collective Behavior. https://arxiv.org/abs/2602.15256

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