  A free-energy minimization approach is used to address the secular &
dynamical instabilities & the bifurcations along sequences of rotating,
self-gravitating fluid and stellar systems. Our approach stems from the
Landau-Ginzburg theory of phase transitions. We focus on the Maclaurin sequence
of oblate spheroids & on the effects of second-harmonic disturbances.
Second-order phase transitions appear on the Maclaurin sequence also at the
points of dynamical instability & of bifurcation of the Dedekind sequence.
Distinguishing characteristic of each second-order phase transition is the
(non)conservation of an integral of motion (e.g. circulation) which determines
the appearance of the transition. Circulation is not conserved in stellar
systems because the stress-tensor gradient terms that appear in the Jeans
equations of motion include viscosity-like off-diagonal terms of the same order
of magnitude as the conventional pressure gradient terms. This explains why the
Jacobi bifurcation is a point of dynamical instability in stellar systems but
only a point of secular instability in viscous fluids. The second-order phase
transitions are discussed in relation to the dynamical instability of stellar
systems, the lambda-transition of liquid He-4, the second-order phase
transition in superconductivity & the mechanism of spontaneous symmetry
breaking.
