Ginzburg–Landau Theory in the Language of Classical Continuum Mechanics: A Pedagogical Atlas of Continuum-Mechanical Analogies, Graded by Strength

Ginzburg–Landau theory, the standard effective description of the superconducting state, admits a precise intuitive vocabulary drawn from nineteenth-century continuum field theory. This atlas organizes that vocabulary across fifteen regimes of the superconducting order parameter and grades every correspondence within a three-tier rigor hierarchy: exact mathematical identity, shared differential structure, and mnemonic analogy. The grading is the central contribution. It separates true functional identities, such as MacCullagh's rotationally elastic medium of 1839 mapping onto the electromagnetic field energy, from correspondences that share only an equation form or a geometric resemblance across different physical spaces. The dictionary extends to the boundary conditions of the functional, where the de Gennes extrapolation length maps onto a Winkler elastic foundation, and to the breakdown of mean-field theory itself, where the Ginzburg fluctuation criterion parallels Lindemann's melting rule. The framework claims no new superconducting results; its originality lies in collecting, grading, and delimiting known correspondences within a single taxonomy. The result is a unified pedagogical reference for advanced undergraduates, graduate students, and instructors.