  Reporting about the density matrix theory for a composite quantum system of
flavor eigenstates, we introduce the idea of flavor-weighted energies. It
provides us with the right correlation between the energies of flavor
eigenstates and their measurement probabilities. In addition, the apparent
ambiguities which follow from computing flavor-averaged energies are
suppressed. The framework of the generalized theory of quantum measurement also
provides some theoretical tools for computing the von-Neumann entropy
correlated to flavor associated energies. It allows for relating flavor
weighted(averaged) energies to non-selective (selective) quantum measurement
schemes. As a final issue, the connection of such flavor associated energies
with the expressions for neutrino effective mass values is investigated. It is
straightforwardly verified that cosmological background neutrino energy
densities could be obtained from the coherent superposition of mass
eigenstates. Our results show that the non-selective measurement scheme for
obtaining flavor-weighted energies is consistent with the predictions from the
single-particle quantum mechanics.
