The Origin of Consciousness as a Constraint-Endogenizing Phase Transition: A Minimal Physical Model

This paper proposes a minimal physical model for the origin of consciousness, framed not as a continuous emergence of complexity or information-processing capacity, but as a one-time, irreversible phase transition in an open, non-equilibrium system. The transition occurs when the constraints that maintain system stability shift from being externally fixed parameters to becoming endogenous dynamical variables—a process termed \textit{constraint endogenization}. Using the language of dynamical systems and phase transition theory, we formally define an order parameter, construct a Landau-type free energy, and introduce stochastic dynamics to demonstrate that this transition is triggered only once, is irreversible, and leaves a permanent topological imprint on the system's phase space. The model provides a non-psychological, non-semantic, and purely physical explanation for the origin of consciousness, offering a clear criterion to distinguish living from non-living systems.