Pedro Maldonado-Lang, Clément Vidal
We explore the emergence of complex structures within reaction networks, focusing on nuclear reaction networks relevant to stellar nucleosynthesis. The work presents a theoretical framework rooted in Chemical Organization Theory (COT) to characterize how stable, self-sustaining structures arise from the interactions of basic components. Key theoretical contributions include the formalization of atom sets as fundamental reactive units and the concept of synergy to describe the emergence of new reactions and species from the interaction of these units. The property of separability is defined to distinguish dynamically coupled systems from those that can be decomposed. This framework is then applied to the STARLIB nuclear reaction network database, analyzing how network structure, particularly the formation and properties of atom sets and semi-self-maintaining sets, changes as a function of temperature. Results indicate that increasing temperature generally enhances network cohesion, leading to fewer, larger atom sets. Critical temperatures are identified where significant structural reorganizations occur, such as the merging of distinct clusters of atom sets and the disappearance of small, isolated reactive units. The analysis reveals core clusters - large (containing more that 1000 reactions), semi-self-maintaining structures that appear to form the core of all potentially stable nucleosynthetic configurations at various temperatures. Overall, the paper provides insights into the structural underpinnings of stability and emergence in complex reaction networks, with specific implications for understanding stellar evolution and nucleosynthesis.