Geodesic
Equations of motion, Green's functions, and thermodynamic relations in theories of linear relaxation with various sets of macroscopic variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 1, pp. 127-138

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A generalized scheme of a theory of linear relaxation in a macroscopic nonequilibrium system is investigated in the case when the set of macrovariables $\operatorname{Sp}P\rho(t)$ is enlarged by the average values of the first, second . . ., and $\alpha$-th time derivatives of the operators $P$ It is shown that for all values of $\alpha$ the same dispersion equation holds for the spectrum of normal modes of the system and also the same infinite system of linear equations. This system contains a finite number of equations of motion of the macrovariables and a hierarchy of equations for the two-time correlation functions which arise in the calculation of the memory function or Green's function. 
@article{TMF_1978_35_1_a12,
     author = {V. P. Kalashnikov},
     title = {Equations of motion, {Green's} functions, and thermodynamic relations in theories of linear relaxation with various sets of macroscopic variables},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {127--138},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a12/}
}
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V. P. Kalashnikov. Equations of motion, Green's functions, and thermodynamic relations in theories of linear relaxation with various sets of macroscopic variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 1, pp. 127-138. http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a12/