Fluctuating hydrodynamics and the thermodynamics of self-gravitating systems

The theory of hydrodynamic fluctuations is applied to a self-gravitating gas in the adiabatic approximation and the correlation functions for the density and velocity are calculated. The theory shows that as the dynamical instability is approached the density fluctuations become large before ordinary stability theory predicts growth. The steady-state solution of the associated Fokker-Planck equation leads, in a natural way, to the appropriate free energy for the system. (author)