Two-Point Non-Equilibrium Correlation Functions

we turn to the calculation of two-point moments. We take the quantities defined by expression (4.7) and average the products of p (t) and pk(t—s), p (t) and pk(t — s), respectively. By taking into account the properties of the equilibrium moments, we find that 

These expressions can be written in a simplified form when inertia effects are not taken into consideration. 

The derivative of the function of instant relaxation is expressed in the delta-function 

These expressions ought to be transformed to eliminate the dependence on the antisymmetrical tensor of the velocity gradients. We can use the new variable v = s — u to rewrite some of the integrals in the above expressions. So, for example, 

Similar transformations allow us to find new expressions for the considered moments 

---