  For a quantum state undergoing unitary Schr\"odinger time evolution, the von
Neumann entropy is constant. Yet the second law of thermodynamics, and our
experience, show that entropy increases with time. Ingarden introduced the
quantum operator entropy, which is the Shannon entropy of the probability
distribution for the eigenvalues of a Hermitian operator. These entropies
characterize the missing information about a particular observable inherent in
the quantum state itself. The von Neumann entropy is the quantum operator
entropy for the case when the operator is the density matrix. We examine pure
state unitary evolution in a simple model system comprised of a set of
highly-interconnected topologically disordered states and a time-independent
Hamiltonian. An initially confined state is subject to free expansion into
available states. The time development is completely reversible with no loss of
quantum information and no course graining is applied. The positional entropy
increases in time in a way that is consistent with both the classical
statistical mechanical entropy and the second law.
