Nonlinear nonequilibrium statistical thermodynamics

A study is made of strongly nonequilibrium systems for which the hypothesis of local equilibrium, on which ordinary linear thermodynamics is based, does not apply. A method is proposed that is valid far from the critical point and allows one in a unified manner to allow for not only the static correlations described by the quasiequilibrium distribution function but also the dynamic correlations associated with the dissipative correction to this function. Zubarev's nonequilibrium distribution function is the mathematical basis of the method. A formula is derived for the mean nonequilibrium fluxes in the second order, i.e., inclusive of the second derivatives and the squares of the first derivatives of the thermodynamic parameters with respect to the coordinates and the time at the point of observation. A method of successive approximations similar to the Chapman-Enskog procedure in the theory of a Boltzmann gas is constructed; it enables one to eliminate the time derivatives of the parameters in the thermodynamic forces in the expressions obtained for the mean nonequilibrium fluxes.