The Invariants of Self-Organizing Systems

Some systems do something that appears to contradict basic physics: they maintain complex organized structure on their own, without external coordination, against the thermodynamic tendency toward disorder. Despite 75 years of work studying such systems across thermodynamics, information theory, dynamical systems, systems biology, and complex systems theory, a 2025 review in npj Complexity notes the field “still lacks the proper conceptual framework to understand it properly” (Gershenson, 2025). This paper provides that framework. We identify seven structural conditions — each established independently in its home discipline, the class named self-organizing systems since Ashby (1947) — that jointly constitute the necessary properties of any self-organizing system. The strongest evidence is not the conditions themselves but their repeated independent discovery: Conservation found in thermodynamics and information theory independently, Attractor Dynamics found in three separate fields by researchers who were not in contact. The conditions are not new. Their joint necessity across all classes of self-organizing systems is.