A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a
reduction of a model from quantum statistical mechanics and also as the
gradient flow of a second-order information functional with respect to the
-Wasserstein
metric. First, we prove global existence of weak solutions for initial conditions of
finite entropy by means of the time-discrete minimizing movement scheme. Second,
we calculate the linearization of the dynamics around the unique stationary solution,
for which we can explicitly compute the entire spectrum. A key element
in our approach is a particular relation between the entropy, the Fisher
information and the second-order functional that generates the gradient flow under
consideration.