  A new kinetic theory Boltzmann-like collision term including correlations is
proposed. In equilibrium it yields the one-particle distribution function in
the form of a generalised-Lorentzian resembling but not being identical with
the so-called $\kappa$ distribution frequently found in collisionless turbulent
systems like space plasmas. We show that this distribution function satisfies a
generalised $H$-theorem, yields an expression for the entropy that is concave.
Thus, the distribution is a `true' thermodynamic equilibrium distribution,
presumably valid for turbulent systems. In equilibrium it is possible to
construct the fundamental thermodynamic quantities. This is done for an ideal
gas only. The new kinetic equation can form the basis for obtaining a set of
hydrodynamic conservation laws and construction of a generalised transport
theory for strongly correlated states of a system.
