  The entropy of a classical thermally isolated Hamiltonian system is given by
the logarithm of the measure of phase space enclosed by the constant energy
hyper-surface, also known as volume entropy. It has been shown that on average
the latter cannot decrease if the initial state is sampled from a classical
passive distribution. Quantum extension of this result has been shown, but only
for systems with a non-degenerate energy spectrum. Here we further extend to
the case of possible degeneracies.
