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For pt. I see ibid., vol. 14, no. 5, 427. The statistical model developed in Part I is applied to the discussion of the stability of inhomogeneous Vlasov equilibria. The existence of instability is expressed by the general condition integral I(x)( theta (x)- phi <sub>0</sub>)dV>0 provided a certain class of variations compatible with the physical constraints imposed on the system does exist. In this criterion I(x) is the information variable depending on the physical system under consideration, phi (x) the corresponding potential, and phi <sub>0</sub> its spatial average. When I(x) is the charge density the criterion can be applied in order to show the instability of the Bernstein, Greene and Kruskal solutions. It is also shown, by means of the entropy principle, that the isolated inhomogeneous collisionless systems evolve towards more homogeneous equilibria, associated with a higher entropy, by transforming their collective energy into the energy of the random individual fluctuations. Moreover, nearly homogeneous but electrostatically unstable collisionless plasmas prove to evolve towards the marginal state of the stable equilibrium (which is a state of maximum entropy for the collisionless systems), while an electrostatic quasi-static marginally unstable mode with long wavelength appears in the system. |
