[machina_ex_deus]

I think it's pretty obvious that the second law comes from reversibility of the microscopic laws.

In classical mechanics, Liouville's theorem makes phase space density incompressible, so you get that entropy always increases. In quantum mechanics, unitarity gives the same incompressibility - the density matrix change with time is multiplying by a unitary matrix left and right, which preserves the eigenvalues, so the entropy, being sum of the log of eigenvalues, stays the same.

The opposite is also obvious: in a system which is irreversible, look at an ensemble of two states which evolve to a single state. The entropy before was 1 bit, after the evolution it's 0 bits. So the system violates the second law.