# Gibbs Free Energy in Superconductors

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1. Mar 3, 2015

### taishizhiqiu

When reading some material concerning Ginzburg-Landau theory of superconductors, I got the following sentence:

The appropriate thermodynamic potential for describing a superconductor in an applied magnetic field is the Gibbs free energy $G$ (natural variable $H$) and not the Helmholtz free energy $F$ (natural variable $B$).

I don't understand the sentence. In gas, Gibbs free energy is minimal in constant temperature and pressure. Does this sentence mean that in superconductors Gibbs free energy is minimal in constant $T$ and $H$? I can't make sense out of it.

2. Mar 5, 2015

### DrDu

L&L discuss quite extensively their peferred thermodynamic variables in the case of magnetic fields in previous chapters.

3. Mar 6, 2015

### taishizhiqiu

You mean Landau and Lifshitz‘s textbook?

4. Mar 6, 2015

### DrDu

Sorry, yes, I had erroneously in mind that you had mentioned Landau & Lifshitz. The relevant pair of variables in case of magnetism is not p and V but B and H and you can analogously define energies and enthalpies with different natural variables.
I think that thermodynamics in the presence of fields is quite a non-trivial matter. Much of the distiction whether B or H are to be preferred depend on the measurement you have in mind and on the chosen separation into system and surrounding, especially, which part of the field belongs where.