Pedro Domingos

The subsystem is either isolated or not. If it's not isolated, the second law doesn't apply. If it's isolated, what I said applies and there's a contradiction with the second law.

No, if a subsystem is isolated, then the subsystem's free Hamiltonian is the total Hamiltonian. Time evolution is governed by the Liouville equation, the Hamiltonian dynamics are unitary, the eigenvalues of the density matrix are conserved, and hence so is its Von Neumann entropy

So the entropy cannot increase and the second law is violated, QED.

The second law: dS≥0 is not violated when entropy is conserved. If the system is coupled to an environment the LVN equation becomes the Lindblad equation, which does not conserve entropy in general, and typically increases the entropy of the subsystem.

The second law is that the entropy of the universe increases in the course of any spontaneous change (Peter Atkins, "The Laws of Thermodynamics", p. 49). So you must be arguing that nothing ever changes, making the law vacuous (and why isn't it dS=0, then?).

theories of physics are relevant within a certain window of scale/energy. The second law is useful to describe any system other than the global wavefunction of the multiverse. It doesn't mean that it's irrelevant at all.

Furthermore, technically the observable universe (any system of interest to humans is within this subsystem) is a subsystem of the universe, due to the Hubble horizon. That makes the observable universe an open quantum system, not closed, and its entropy increases over time.

As you know, what happens beyond the Hubble universe can’t possibly affect us, so no, the observable universe is a closed system, and yet it changes spontaneously and its entropy doesn’t increase. So the second law is false.