Normalized Free Energy and Normalized Entropy Applied to Some Lambda (λ) Transitions

The λ-anomaly occurs for a system that can undergo a boson – fermion thermodynamic equilibrium. It is shown that a λ-transition figure can be interpreted in terms of the normalized Gibbs–Helmholtz equation, the Maxwell–Boltzmann energy distribution function, and properties of the statistics of the relevant species. There are three variations of a “λ-transition” curve. These are: (A) the classical λ curve, (B) a saw-tooth line shape that is characteristic of the Bardeen–Cooper–Schrieffer theory of superconductivity, and (C) a single line δ type figure. The low temperature He-4 transition, and Type II superconductor transitions are typical of the line shape A. Type I superconductors typically have type B line shapes. The line shapes for variations A and C result from classical thermodynamic equilibria. The type B line shape occurs in systems that do not have a classical thermodynamic equilibrium at the superconducting transition. Analysis of type B line shapes provides interesting concepts and data for some low- and high-temperature superconductors. Several applications and physical property consequences of these line shapes are discussed.