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According to The statistical nature of the 2nd Law of Thermodynamics, the second law of thermodynamics probably hasn't been proven to be absolute. That doesn't necessarily mean it hasn't been proven that a perpetual motion machine of the second kind is impossible. It follows from the second law of thermodynamics that it's impossible but does not follow the other way.

The question Perpetual motion machine of the second kind possible in nano technology? doesn't have an answer that I think satisfactorialy answers this question. I think this answer could be wrong because the second law of thermodynamics probably hasn't been proven to be absolute. Some of its other answers probably satisfactorily answer that question but not this one.

Timothy
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There are two ways to derive the second law. One way uses microstates, probabilities, and statistics (this is how physicists would think about it) and the other way uses bulk properties (and is the way most engineers are taught the subject); see Thermophysics by Giedt, in which he does the derivation both ways- with the same result.

The fact that the derivation can be performed without microstates and statistics strongly suggests that your assertion that the 2nd law is "strictly statistical" in nature can be argued to be untrue.

Regarding your nanotechnology claim, have a look at treatments of something called "Maxwell's Demon". You'll see how nanotechnology fundamentally cannot beat the second law.

niels nielsen
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Turbulent motion of water in an electric field:

https://www.youtube.com/watch?v=17UD1goTFhQ

https://www.youtube.com/watch?v=T6KAH1JpdPg

The motion is powered by:

(A) electric energy?

(B) ambient heat?

If (B) is the answer (it is!), the second law of thermodynamics is violated - the work the motion is obviously able to do (e.g. by rotating a waterwheel) will be done at the expense of heat absorbed from the surroundings.

Pentcho Valev
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