I’m not a cold fusion expert but my understanding of it is that it quite grossly violates the first law at least. If the first law is out, thermodynamics as we know it is wrong.
Muon catalyzed cold nuclear fusion is a thing. You're going to pour more energy into creating the muons than you get out though. It doesn't violate thermodynamics, you're just using some kind of catalytic process to get past the fairly massive energy barrier between getting those nuclei close together. You're still gaining net energy from the overall reaction itself. Catalytic reactions don't violate thermodynamics (unless that's really why there's so much catalytic converter theft because you can build perpetual motion machines out of them).