From weak coupling to geometric buoyancy: Tc scaling theory

In this paper, we propose a new phenomenological interpretation of the superconducting transition based on the topology of the phase space. The concept of "Geometric condensate buoyancy" is introduced, according to which the thermodynamic stability of a superconducting state is determined not only by the microscopic pairing potential, but also by the global metric capacity of the phase space available for the formation of a coherent state. A universal critical temperature equation is derived based on the principle of topological scaling. The paper presents the derivation of a geometric invariant for systems of various dimensions (2D, 2.5D, 3D). The theory has been verified on a wide range of materials: from classical metals (Al, Pb) and MgB2 compounds to high-temperature cuprates (YBCO, Bi-2212) and pressurized hydrides (LaH10). The proposed model provides a geometric explanation for the anomalous Pb parameters and establishes a theoretical limit of the critical temperature for carrier-deficient systems such as FeSe.Note: The English version was automatically generated and may contain inaccuracies.