Gibbsian theory of power law distributions

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.