A maximum entropy principle for the equilibrium distribution of quantum state wavefunctions

From the perspective of statistical mechanics, quantum system properties emerge as an average of an ensemble of single system states. It is well known that at thermal equilibrium, the observable properties of quantum systems obey a Gibbs state distribution, i.e., Boltzmann distributed energy eigenvalues. However, the associated ensemble of system wave functions cannot be formulated in analogy to classical systems, i.e., as a maximum entropy distribution subject to a constraint on the mean energy expectation value. Instead, the properties of thermal equilibrium are satisfied by the so-called "Scrooge ensemble" — the ensemble of minimal accessible information. We demonstrate that this ensemble can be derived via a maximum entropy principle.