Noncumulant projection and elimination of time derivatives from the nonequilibrium distribution function

Time-independent projection operators are introduced, the action of which on the non-equilibrium distribution function leads to quasi-equilibrium function. These projection operators single out in a consequtive way the contributions from unconnected diagrams and so they may be called non-cumulant. By means of the non-cumulant projections the time derivatives are removed from the non-equilibrium distribution function. This is performed for the most general case of hydrpdynamic theory, i.e. in any order with respect to the amplitude deviations from the equilibrium and with the spatial and time dispersion completely taken into account. The final expression for the nonequilibrium distribution function contains explicitly the contributions of connected diagrams only. With the aid of the technique developed, the equations of the nonlinear and non-local in time and space hydrodynamics obtained earlier on the basis of the Mori projection operators, are transformed to the explicitly connected form. Then the equivalence between these equations and the equations obtained on the basis of the non-cumulant projection operators is established.