chapter  41
3 Pages

Strongly non-equilibrium states and the structure of transport equations

The formulated structure of the complete system of equations (38.6) and (38.7) allows, as a solution, to obtain, as a function of time, the average values of the five dynamic variables 〈Sf〉 and their 15 pair combinations 〈Sfg〉 (see Appendix 2). These equations represent a microscopically modified hydrodynamic theory of mass, impulse, and energy transfer due to allowance for fluctuations arising when the flow velocity increases, and the kinetic theory of mean square fluctuations of dynamic variables describing the processes of mass, impulse, and energy transfer. The theory relies on closed expressions for the decoupling of multiparticle probabilities through unary and paired DFs and does not have a small thermodynamic parameter (in contrast to the approaches discussed in Ref. [56]), and can therefore be used for various strongly non-equilibrium processes. Introducing in the usual way [57], deviations of one dynamic variable ∆Sf = Sf − 〈Sf〉, and their standard deviations as ∆Sfg = 〈Sf-〈Sf〉〉 (Sg− 〈Sg〉) = 〈Sfg〉 −〈Sf〉〈Sfg〉, as a result of the solution of the constructed system of equations, the time dependences of the root-mean-square fluctuations of the dynamic variables Sf will be obtained. In contrast to the correlation functions that can be introduced for one or two different times [1,36,46], all the new 15 dynamic variables 〈Sfg〉 refer to one time point that corresponds to the time scale of the evolution of the variables 〈Sf〉.