We have recently obtained some interesting results on the global stability characteristics of gaseous and stellar systems using a free–energy variational formulation and Ginzburg–Landau phase transition theory (Christodoulou et al. 1995a, b). For m = 2 nonaxisymmetric modes in particular, we have been able to formulate a new, robust, global stability criterion (Christodoulou, Shlosman, & Tohline 1995, hereafter CST) that avoids many of the problems that plagued the well–known Ostriker & Peebles (1973) criterion. In this article, we briefly summarize the conclusions from the above–cited investigations and we proceed to comment on the stability properties of some interesting stellar models that were discussed during this conference and that are not trivially understood in terms of the new stability criterion.
The thermodynamic stability criterion in a self-gravitational system with phase transition