Statistical Mechanics of Stable States Far from Equilibrium: Thermodynamics of Turbulent Plasmas

Abstract

This paper reviews some recent developments in the theory of stationary states 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 when the plasma evolves into a highly nonlinear state entirely dominated by wave generation, wave-wave and wave-particle interaction and generating a nearly stationary level of turbulence. Sometimes it is very difficult to describe the evolution of such a state. The present theory shows that it is nevertheless possible to develop a macroscopic picture in the framework of statistical mechanics and thermodynamics which allows for the macroscopic description of such states. This can be achieved introducing a control parameter κ. The equilibrium distribution which replaces the Maxwell-Boltzmann distribution is a generalized Lorentzian orκ-distribution. We sketch the underlying statistical mechanics and provide some arguments for the validity of this approach. On this level it is not possible to obtain a microscopic theory of κ, however, which must be constructed on the way of referring to the particular kind of turbulence. We note a number of unresolved problems.