Now you've done it, I'll have to go dig up that book which has a long-form detailed derivation of 2-T - which I accept. I DO NOT accept the common oversimplification taught to kids in science class, however.
The "real" statement makes the assumptions explicit (over time, in the absence of non linearities in the system and so on) - and in some systems, those assumptions are not satisfied, hence the rest doesn't apply as it would were all the assumptions true. That's the angle I'm attacking this from. It's not like 2T is dead wrong, it's like Newton, then we discover e=mc2 and stuff like that. Only in this case, its classical vs quantum, working in a region where neither of the math-sets work very well, and the "splice" function isn't very well defined, so there's some hope here. Or so I think. In fact, I once did a very careful study of 2T to discover what the assumptions were so I could perhaps find a way to make them not the case, to enable such flights of fancy. I've stated the important ones above.
"On average". 2T allows for things that are "transitory". It just says what the equilibrium will wind up being.
"Nothing nonlinear" - most always the case in nature (but not around black holes, or Hawking radiation wouldn't exist), but not if you do something to deliberately make nonlinearity happen. This provides the possibility of changing "transitory" to "permanent" if you can make energy flow one way with some sort of "check valve" - be it a photon that radiates out of the system, or a diode - or something entirely else.
Someone imagined and built a tiny watch escapement - a mechanical ratchet-diode. Put it in warm water, the thing turns all the time, just one way (no obvious temperature drop in the system anywhere) - and you can see why, clearly. Some big surprises have happened at the nanoscale, where things get interesting in the tug of war between quanta and classical smoothness. In this case, any random fluctuation of atomic jiggling that happens to put force on the wheel in the correct direction can move it. The rest of the time, the ratchet holds it. So you can "select from random data" and be successful with doing it. I just think the floating magnet thing scales better, since you could in principle do it with silicon fab technique we have already.