Statistical mechanics of stable states far from equilibrium: Thermodynamics of turbulent plasmas

This paper reviews some recent developments in the theory of stationary sta tes in collisionless media that are very far from thermal equilibrium. Such states may evolve under conditions when the binary collision time is much longer than any characteristic time of the processes under consideration. A typical example of such a system is collisionless turbulence in a plasma w hen the plasma evolves into a highly nonlinear state entirely dominated by wave generation, wave-wave and wave-particle interaction and generating a n early stationary level of turbulence. Sometimes it is very difficult to des cribe the evolution of such a state. The present theory shows that it is ne vertheless possible to develop a macroscopic picture in the framework of st atistical mechanics and thermodynamics which allows for the macroscopic des cription of such states. This can be achieved introducing a control paramet er kappa. The equilibrium distribution which replaces the Maxwell-Boltzmann distribution is a generalized Lorentzian or kappa -distribution. We sketch the underlying statistical mechanics and provide some arguments for the va lidity of this approach. On this level it is not possible to obtain a micro scopic theory of kappa, however, which must be constructed on the way of re ferring to the particular kind of turbulence. We note a number of unresolve d problems.