Toward a General Theory of Phase Transitions : A Comparative Study of Self-Organizing Systems Based on Invariant Structures and Degrees of Freedom

This study proposes a theoretical framework for understanding phase-transition-like phenomena that are commonly observed across cosmological, social, biological, and artificial systems. While phase transitions have traditionally been treated as domain-specific phenomena, this work redefines them not as energy-driven events, but as structural reconfigurations of degrees of freedom and interaction networks. To this end, a five-dimensional state space consisting of density, connectivity, interaction strength, propagation speed, and degrees of freedom is introduced to describe system states in a structural manner. Furthermore, the existence of structural and functional invariants that may be preserved before and after phase transitions is hypothesized, and these invariants are positioned as an analytical foundation for comparative systems science. In addition, phase transitions are interpreted not as phenomena governed by a single critical condition, but as emergent consequences of changes in control capacity resulting from the redistribution of constraints and degrees of freedom. This formulation enables a comparative theoretical description of self-organizing systems across different scales. This study does not aim to provide a cosmological explanation of the universe. Instead, it proposes a methodological framework for constraining the properties of unobservable regimes through the extraction of invariant structures common to complex systems.