Energy transduction in complex networks with multiple resources: The chemistry paradigm

We extend the traditional framework of steady state energy transduction—typically characterized by a single input and output—to multi-resource transduction in open chemical reaction networks (CRNs). Transduction occurs when stoichiometrically balanced processes are driven against their spontaneous directions by coupling them with thermodynamically favorable ones. However, when multiple processes (resources) interact through a shared CRN, identifying the relevant set of processes for analyzing transduction becomes a critical and complex challenge. To address this, we introduce a systematic procedure based on elementary processes, which cannot be further decomposed into subprocesses. Our theory generalizes the methodology used to define transduction efficiency in thermal engines operating between multiple heat baths. By selecting a reference equilibrium environment, it explicitly reveals the inherently relative nature of transduction efficiency and ties its definition to exergy. This framework also allows one to exclude unusable outputs from efficiency calculations. We further extend the concept of chemical gears to multi-process transduction, demonstrating their versatility as an analytical tool in complex settings. Finally, we apply our framework to central metabolic pathways, uncovering deep insights into their operation and highlighting the crucial difference between thermodynamic efficiencies and stoichiometric yields.