Environment-Driven Emergence of Higher-Order Collective Behavior

TL;DR

This paper demonstrates that higher-order collective behaviors can emerge from shared stochastic environments without direct interactions, highlighting environmental mediation as a distinct organizational mechanism.

Contribution

It introduces a minimal stochastic model showing environment-driven emergence of higher-order structures and establishes a no-go theorem for static environmental coupling.

Findings

Environmental fluctuations induce redundant and synergistic dependencies.

Time-dependent environmental coupling can generate transitions between redundancy and synergy.

Shared environments can produce higher-order organization beyond direct interactions.

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.