Cobb-Douglas models interpreted by Biology: from Kleiber’s Law to thermodynamic foundations of production

The so-called Cobb–Douglas production function offers a synthetic mathematical formalization of economic activity. Focused primarily on capital and labor, it systematically overlooks the role of natural resources and the environment—an omission that has made it the target of recurring criticism. To examine the validity of these critiques, this article proposes a parallel with Kleiber’s law in biology, which links an organism’s energy consumption to its body mass through the notion of basal metabolic rate. We demonstrate that this analogy opens the way for a reinterpretation of both the Cobb–Douglas function and the Solow model, enabling a perspective that is not only compatible with but also complementary to ecological economics. Moreover, it reveals a deeper homology: in both cases, the functions describe the behavior of dissipative thermodynamic systems, which organize energy flows to sustain their structural integrity. This framework allows for a physical reading of economic production mechanisms—not as abstract aggregates, but as expressions of a universal process of self-organization driven by flows of matter and energy. It enables the integration of thermodynamic constraints into the core of economic theory, in continuity with existing literature, while paving the way for an understanding of the economy as a physically evolving system