Statistical theory of nonlinear hydrodynamic fluctuations of ion systems

For ionic system on the base of Fokker–Plank equation for the distribution function of coarse-grained dynamic variables (mass density, charge density, momentum density, current density and total energy) the equations for time correlation functions are obtained. Calculations of the statistical weight, thermodynamic forces and hydrodynamic velocities bots in gaussian and higher approximations are carried out. The expressions for generalized transfer coefficients depending on $k$ and $\omega$ whith distinguished contributions of fluctuations are found.