Is the second law of thermodynamics fundamental? Like Newton's laws for example. I'm having doubts about the increase of entropy of any system. Poincaré stated the recurrence theorem which goes against the increase of entropy of a dynamical system with respect to time. By this theorem, a dynamical system will return at its original state after a finite amount of time, even if it's a really really really big amount of time. Entropy says that irreversible processes are one way and that these processes are really irreversible, while the recurrence theorem implies that there's no irreversible process. (Okay, with several assumptions, like a finite size Universe and some others). I know that Boltzmann and Zermelo took different positions over the subject of the second's law, but I can't find the letters they wrote to each other. Now I'm asking a question I really would like to know the answer : Does Quantum Mechanics solves the problem of entropy? For instance I don't think the recurrence theorem takes into account that a particle can disappear (I think QM does, but I'm unsure since I didn't study it yet), or any other "strange" stuff to Classical Mechanics. And by this the recurrence theorem wouldn't be of a good use to apply to the Universe since it doesn't take into account important realities of the Universe. Does QM offers a proof that the entropy of any system really increase with respect to time? I know I'm not qualified at all (currently studying introductory thermodynamics at university), but these questions I ask are important to me, so that I can imagine better all what I'm learning. And understand how things really are. Thanks very much.