We can prove that gibbs entropy is preserved from Liouville's theorem. We can also prove that its conserved from Noether's theorem and the time reversal symmetry of the Hamiltonian.
But it seems intuitively also that we can prove Liouville's theorem from gibbs entropy conservation, and hence from Noether's theorem. In fact, just setting a uniform distribution seems to me to directly give you Liouville's theorem from gibbs entropy conservation.
Is my understanding correct?
