On details of the thermodynamical derivation of the Ginsburg--Landau equations

TL;DR

This paper clarifies the thermodynamical derivation of the Ginsburg--Landau equations, highlighting its limitations and applicability only to isolated superconducting specimens, resolving ambiguities in existing textbooks.

Contribution

It provides a detailed clarification of the derivation process and explicitly states the validity range of the thermodynamic Ginsburg--Landau theory.

Findings

Thermodynamic derivation has been clarified and formalized.

The theory is valid only for superconductors not part of an external current loop.

Existing textbooks contain contradictory interpretations that are addressed.

Abstract

We examine the procedure of thermodynamical derivation of the Ginsburg--Landau equation for current, which is given unclear and contradictory interpretations in existing textbooks. We clarify all steps of this procedure and find as a consequence a limitation on the validity range of the thermodynamic Ginsburg--Landau theory, which does not seem to be explicitely stated up to now: we conclude that the thermodynamic theory is applicable only to a superconducting specimen that is not a part of an external current-carrying loop.