  A class of non-Markoffian nonunitary models for Newtonian gravity is
characterized as following from some rather natural hypotheses. One of such
models was previously obtained as the Newtonian limit of a classically stable
version of higher derivative gravity. They give rise to a mass threshold around
$10^{11}$ proton masses for gravity induced localization, to a breaking of
linearity and to the possible identification of thermodynamic and von Neumann
entropies.
