If you have experimental background in fluctuations in HTS materials, I would like to know briefly what superconducting quantity you worked with, and also what you relied on for conclusive evidence that what you were seeing is, in fact, fluctuation phenomena. Please consider providing a citation to any publications that go along with your answer.
Virtually all texts on statistical physics make an excursion into fluctuations in the context of ensemble equivalence. For example one can find a rigorous expression connecting the heat capacity with the energy fluctuations of a system. In the context of ensemble equivalence one can use this expression to show that in the thermodynamic limit N-> infinity the relative energy fluctuation go to zero so the energy of a system in contact with a heat reservoir is essentially sharp and thus there is equivalence to the microcanonical ensemble. This is just a side remark.
The relation between heat capacity and energy fluctuation can be interpreted as a relation between fluctuations (of energy) and a response function (heat capacity measures temperature response of a system on heat influx). This is a special case of the celebrated fluctuation-dissipation theorem which in general connects fluctuations expressed by correlation functions through a response function (specifically the imaginary part of the complex response function). I would argue that still the best source for this is the Landau-Lifshitz volume 5 (I think it is). It is somewhat abstract. I found it very instructive to have first a look to a simple analogue from classical mechanics. The damped harmonic driven oscillator can be considered in the framework of the fluctuation dissipation theorem. It is straightforward to calculate the complex amplitude as a response to the driving force and one can calculate the dissipated energy per cycle and find a relation. Some are more inclined to electrical engineering. In this case one may want to start with looking at telegraph noise. Both is a good preparation to fill the most general fluctuation-dissipation theorem with life.
Thanks for the detailed response Christian. As luck would have Vol 5 is the only volume of L&L that I have in my possession. I will review it carefully. Now that you have equipped me with this strong background, I will expose a little more motive for my question. I have found that the microwave nonlinear response of some high temperature superconducting samples appears to persist for as much as 1K above the Tc. I postulate that either I don't really know the Tc very accurately, or this is a manifestation of fluctuation phenomena. It is most likely the former since I am not at all capable in transport measurement and I don't know that the Tc can be as accurately found from microwave response. But I am looking for ideas for testing the ladder.
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