Statistical Mechanics of Two‐dimensional Vortices and Collisionless Stellar Systems

Abstract

In this article, we stress the analogy between two-dimensional vortices and collisionless stellar systems. This analogy is based on the similar morphology of the Euler and Vlasov equations. These equations develop finer and finer filaments, and a description is appropriate to smooth out the fluctuations and describe the macroscopic evolution of the system. We show here that the two descriptions are similar and apply the methods obtained in two-dimensional turbulence to the case of stellar systems. In particular, we propose a new evolution equation for the coarse grained distribution function based on a general maximum entropy production principle. This equation (of a generalized Fokker-Planck type) takes into account the incompleteness and the statistical degeneracy of the violent relaxation and should be able to model the evolution of collisionless stellar systems.