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# A General, Measurable Definition of Emergence (E = ΔO)

Cabrera D, Journal of Systems Thinking 5(1):1-23, 2025

## Abstract

Emergence is central to systems science, yet its definition remains fragmented, domain-specific, and often metaphorical. Existing accounts—including weak and strong emergence, interactionist models from complexity science, and physics-based descriptions of phase transitions—do not provide a general mechanistic operator that links structural change to behavioral change in a measurable way. This paper develops a formal, domain-independent definition of emergence grounded in O-Theory, which models system organization (O) through the structural patterns of Distinctions, Systems, Relationships, and Perspectives (DSRP). We define emergence as the change in system behavior resulting from a change in system organization, formalized as E = ΔO. To evaluate this definition empirically, we analyzed the full Congressional Record from January 2019 and January 2020. Organizational structure was quantified using LLM-based DSRP coding, supported by a dedicated reliability study (median test–retest r = .98). Behavioral divergence was measured using Kullback–Leibler (KL) divergence. The results show clear structural reorganization (ΔO > 0), substantial behavioral divergence (KL = 0.3487), and a stable dependency between organizational load and behavioral variation across models and years. Together, these findings demonstrate that emergence can be operationalized as a structural–behavioral dependency in real-world cognitive–linguistic data, providing a generalizable, mechanistic, and empirically verifiable account of emergent phenomena.

[Read the paper](https://doi.org/10.54120/jost.v25i1.dc6gmde6)