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 for instance fully developed turbulence. The probability distribution function and thermodynamic potentials are obtained. As a side product Fermi and Boson distributions in such hypothetic states are constructed as well, and it is shown that they have no zero-temperature limit, which is in agreement with that the present theory holds under high temperature conditions only.