Thermodynamic and magnetic measurements serve as primary probes for determining the superconducting gap structure in complex materials. A pervasive method for analyzing such data is the phenomenological single-gap \(\alpha \) -model, which adjusts the coupling strength \(\alpha = \varDelta (0)/k_B T_c\) to fit deviations from the BCS weak-coupling limit. However, this approach inherently neglects interband scattering, a microscopic mechanism essential for thermodynamically locking distinct Fermi surface sheets to a single critical temperature. In this work, we present a comparative theoretical analysis of the electronic specific heat and the lower ( \(H_{c1}\) ) and upper ( \(H_{c2}\) ) critical magnetic fields calculated within the \(\alpha \) -model versus the microscopic self-consistent two-gap model derived via the Bogoliubov-Valatin transformation. By applying both frameworks to iron-based superconductors – including LiFeAs, Ba(Fe \(_{1-x}\) TM \(_x\) ) \(_2\) As \(_2\) (TM = Co, Ni), and SmFeAsO \(_{0.9}\) F \(_{0.1}\) – as well as the noncentrosymmetric superconductor BeAu, we demonstrate that neglecting interband coupling leads to fundamental physical inconsistencies. Specifically, we show that the anomalous specific heat shapes often observed (suppressed jumps and low-temperature humps), alongside the distinct multi-scale curvatures and low-temperature saturation plateaus in \(H_{c1}\) and \(H_{c2}\) , are natural thermodynamic consequences of "passive" bands where superconductivity is induced via the proximity effect in momentum space. We conclude that while the \(\alpha \) -model offers fitting flexibility, the self-consistent evaluation of coupled gap equations is strictly required to extract physically reliable gap magnitudes, spatial coherence scales, and coupling potentials ( \(\varLambda _{ij}\) ) from the bulk responses of multiband systems.
