A statistical mechanical view of complex economies under the green transition

TL;DR

This paper models complex economies under the green transition using statistical mechanics, revealing phase transitions that delineate viable economic activity from shutdown regimes influenced by waste and technological constraints.

Contribution

It introduces a novel statistical mechanics framework for analyzing the tradeoffs in sustainable economic development, explicitly incorporating waste as a key variable.

Findings

Identifies a double phase transition separating viable and shutdown regimes.

Greener economies support fewer technologies but achieve higher welfare.

Rapid growth under waste constraints can destabilize economic systems.

Abstract

We propose a stylized model of a complex economy to explore the economic tradeoffs imposed by the so called "green transition" -- the shift towards more sustainable production paradigms -- using tools from the Statistical Mechanics of disordered systems. Namely, we promote the parameters of a standard input-output economic model to random variables, in order to characterize the typical statistical properties of its equilibria. A central feature of our work is the explicit inclusion of a waste variable as a proxy for the unwanted byproducts, such as emissions, generated by different production processes. We find that the interplay between economic development and waste gives rise to a double phase transition, separating a region of viable economic activity from two distinct shutdown regimes. Notably, more wasteful ("brown") economies support a larger number of technologies per good but fail to activate most of them, limiting their productive capacity. In contrast, "greener" economies, while having access to fewer technologies, tend to achieve higher economic welfare, up to a critical point where rapid growth under tight waste constraints may destabilize them. Our results highlight the structural tensions between technological development and environmental sustainability, suggesting that the green transition may require careful navigation to avoid abrupt collapses in economic activity. The nature of the phase transitions we observe in the model is linked to the shrinkage of feasible economic configurations under increasing constraints, akin to algorithmic phase transitions studied in Computer Science.