  The stratification of entropy and the stratification of angular momentum are
closely analogous. Of particular interest is the behavior of disks in which
angular momentum transport is controlled by convection, and heat transport by
dynamical turbulence. In both instances we argue that the transport must
proceed ``backwards'' relative to the sense one would expect from a simple
enhanced diffusion approach. Reversed angular momentum transport has already
been seen in numerical simulations; contra-gradient thermal diffusion should be
amenable to numerical verification as well. These arguments also bear on the
observed nonlinear local stability of isolated Keplerian disks. We also
describe a diffusive instability that is the entropy analogue to the
magnetorotational instability. It affects thermally stratified layers when
Coulomb conduction and a weak magnetic field are present. The criterion for
convective instability goes from one of upwardly decreasing entropy to one of
upwardly decreasing temperature. The maximum growth rate is of order the
inverse sound crossing time, independent of the thermal conductivity. The
indifference of the growth rate to the conduction coefficient, its simple
dynamical scaling, and the replacement in the stability criterion of a
conserved quantity (entropy) gradient by a free energy (temperature) gradient
are properties similar to those exhibited by the magnetorotational instability.
