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

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