Really enjoyed reading this. If I may, I would like to point out that several modern papers have started describing fluctuations as an exception to second law, which IMHO is not correct. Fluctuations are infact derived from the second law, i.e. that entropy should always increase and that an equilibrium represents a state of maximum entropy. However, fluctuations exists because this entropy is a potential and hence have a continuous second derivative/ curvature (convex). In order, for the system to be able to attain the maximum it needs to be able to scope the nearby states, which are the fluctuations.

Any decrease in entropy due to these fluctuations are local and momentary, which is not the entropy that the second law is defined for as the second law doesn’t have time and space, i.e. the limits on the integeral are infinite, or so large that no perceptible change occur any more. In other words, the second law is for macroscopic entropy. See for example, Einstein’s 1910 paper on fluctuations and critical opalascence.

Microscopic fluctuations, which are often cited as exceptions are not exceptions, because fluctuations by definition are reversible, hence entropy in principle is constant, or we haven’t defined the system properly.