PARADIGM SHIFT IN THE THEORY OF COHERENT STATES: FROM LANDAU'S THERMODYNAMIC FREEZING TO KURAMOTO'S DYNAMIC PHASE LOCKING.

This work exposes a fundamental conceptual impasse in the classical phenomenological theory of phase transitions developed by Landau and the mean-field approximation, particularly in the context of the search for high-temperature superconductivity. We demonstrate that brute-force cooling () encounters an insurmountable quantum-topological limit: the internal confinement entropy of the proton (), which makes the complete elimination of fluctuations in equilibrium systems impossible. As an alternative, we propose the framework of Phase Dynamics, which translates the description of macroscopic coherence from the language of static order parameters to the language of dynamic phase locking in non-Euclidean topological manifolds. We show that when the Kuramoto coupling constant exceeds a critical threshold (), a second-order phase transition to a globally coherent state occurs. This dynamic phase locking leads to the asymptotic vanishing of the dissipative components of the energy-momentum tensor, providing a pathway to macroscopic quantum coherence at arbitrary temperatures, completely bypassing the need for cryogenic freezing.