Statistical derivation of the equations of motion of second-order liquids

The equations of motion are derived of second-order liquids, i.e., slightly non-Newtonian liquids for which it is sufficient to take into account only the quadratic terms in the velocity gradients in the stress tensor. The derivation is based on the nonequllibrium statistical distribution of Zubarev and McLennan. The expression for the stress tensor contains three new constants that do not appear in the ordinary stress tensor. These new constants are expressed in terms of the double and triple time correlation functions. It is noted that a similar derivation by Storer and Green [9] led to incorrect results. The dimensionless parameters in the expansion of the stress tensor are found by means of an estimate based on the assumption that the fluctuations of the microscopic quantities represent a Gaussian Markov process.