  Assuming that the interacting neutrino and the solar matter can be treated as
an open quantum system we formulate a formalism of neutrino state evolution in
terms of the Bloch vector, obtained by solving a quasilinear extension of the
von Neumann equation. We broaden the classical Wolfenstein formalism by means
of exploiting the strictly linear von Neumann equation and reinterpreting the
results in terms of the quantities appropriate for the quasilinear approach. We
obtain similar predictions for the averaged neutrino survival probability
measured on Earth in both approaches, differing by details inside the Sun where
the quasilinear evolution predicts a suppression of oscillations. We discuss
the issues of energy transfer between the neutrino and the Sun and the speed of
the state evolution in both approaches.
