  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.
