Seeing global trade through the lens of physics

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New research from the Complexity Science Hub (CSH) shows why widely used algorithms for measuring economic complexity produce trustworthy results and how these tools may benefit diverse areas such as ecology, social science, and agentic AI. The paper is published in the journal Physical Review E.

What determines whether a country can successfully develop new industries or why some economies diversify while others remain dependent on a few exports?

For more than a decade, researchers studying global trade have relied on so-called economic complexity algorithms to approach questions like these. Instead of analyzing hundreds of economic indicators, these methods look at something quite simple: they measure a country's potential based on the sophistication of what it exports. If a country successfully exports more complex products, it rises within complexity rankings. While the rankings proved effective, the principles driving them were not fully understood.

Now, the new study provides a deeper understanding of how these tools actually work and why their results can be trusted. The research, led by Alessandro Bellina (Centro Ricerche Enrico Fermi, Sony Computer Science Laboratories Rome, Sapienza University of Rome), Paolo Buttà (Sapienza University of Rome) and Vito D. P. Servedio, faculty member at the Complexity Science Hub, reinterprets economic complexity algorithms through the lens of physics. Their work shows that the rankings produced by these methods emerge from the same principles that govern physical systems seeking states of minimal energy.

Why do economic complexity algorithms work?

Economic complexity methods aim to estimate a country's productive capabilities. The algorithms analyze a global network linking countries and the products they export. From this structure, they generate rankings according to their complexity.

"These rankings are often used to explore how economies might evolve or which industries could realistically emerge next," explains Vito D. P. Servedio. "Countries may use this type of analysis when thinking about long-term investment strategies." Despite their widespread use, an important theoretical question had remained unresolved: why do these algorithms work at all?

Proving there is only one answer

Two approaches dominate the field: the Economic Complexity Index (ECI) and the Economic Fitness and Complexity algorithm (EFC). Both rely on iterative calculations that gradually converge toward a ranking. Until now, however, researchers could not formally prove whether these calculations always lead to a single stable result.

"That matters," says Servedio. "If different solutions were possible, policymakers or researchers could end up drawing completely different conclusions from the same data."

The new study resolves this uncertainty especially for the non-linear and more mathematically challenging Fitness algorithm (EFC). By reformulating it as an optimization problem, the researchers showed that the system behaves like a ball rolling inside a perfectly shaped bowl: it inevitably reaches the same minimum point, which means that the underlying structure is strictly convex. For Servedio, this convexity is something "beautiful."

Two algorithms, two physical dynamics

Viewing the algorithms through the lens of physics also revealed an unexpected insight: the two approaches describe fundamentally different dynamics. The Economic Complexity Index (ECI) behaves like a harmonic system connected by springs, pulling similar economies closer together. It tries to minimize the difference between connected nodes.

The Fitness approach (EFC), by contrast, introduces repulsive effects that emphasize differences and structural limits within the trade network. This distinction is crucial when analyzing the "energy" of individual trade links. When the researchers applied this "energetic framework" to real-world data (UN COMTRADE), they saw something striking: this perspective highlights areas where the system is under stress.

"We can now visualize the stress in the trade network," Servedio emphasizes. These high-energy links represent the fragile points in global trade networks and points where a shock could cause a network to collapse.

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Practical benefits beyond economics

Reframing the algorithms as energy-minimization problems also leads to a practical advantage: computations can reach results significantly faster by directly following the underlying energy landscape instead of relying on iterations. While this speed difference matters little when analyzing only a few countries, it becomes relevant in large-scale systems.

Although developed for international trade, the methods can be applied to other types of complex networks, such as technological ecosystems, infrastructure networks or special economic analysis. For example, for diagnosing fragility and understanding how disruptions propagate through networks. Furthermore, the research team noticed similarities to agentic optimization methods currently discussed in artificial intelligence research. The main contribution of the study, however, is conceptual.

"It will not change the decisions policymakers make," Servedio says. "But they can now be sure these tools will not deliver unrealistic results."

Publication details

Alessandro Bellina et al, Cost functions in economic complexity, Physical Review E (2026). DOI: 10.1103/tgcg-8hw2

Journal information: Physical Review E

Provided by Complexity Science Hub