Kinetic theoretical foundation of Lorentzian statistical mechanics

A new kinetic theory Boltzmann-like collision term including correlations i s 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 tu rbulent systems like space plasmas. We show that this distribution function satisfies a generalised H-theorem, yields an expression for the entropy th at 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 do ne for an ideal gas only. The new kinetic equation can form the basis for o btaining a set of hydrodynamic conservation laws and construction of a gene ralised transport theory for strongly correlated states of a system.