  It is shown that power law phase space distributions describe marginally
stable Gibbsian equilibria far from thermal equilibrium which are expected to
occur in collisionless plasmas containing fully developed quasi-stationary
turbulence. Gibbsian theory is extended on the fundamental level to
statistically dependent subsystems introducing an `ordering parameter'
$\kappa$. Particular forms for the entropy and partition functions are derived
with super-additive (non-extensive) entropy, and a redefinition of temperature
in such systems is given.
