A case of thermodynamic failure in the Ginzburg--Landau approach to fluctuation superconductivity

Abstract: The Ginzburg--Landau approach postulates an energy density, together with an interpretation for the supercurrent, and invokes Ohm's law. We consider quasi-one-dimensional nonuniform superconducting loops, either smooth or piecewise uniform, that enclose a magnetic flux, above the critical temperature. We evaluate the averages of the current and of the power released per unit length, due to thermal fluctuations. We consider three averages: canonical ensemble average, time-average using a time-dependent model, and canonical ensemble in the reciprocal space. All the evaluations imply that heat is absorbed in part of the loop and released in other part, despite the assumption that the loop is at uniform temperature.