Geodesic
Zubarev's nonequilibrium statistical operator method in the~generalized statistics of multiparticle systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 1, pp. 71-89

Voir la notice de l'article provenant de la source Math-Net.Ru

We present a generalization of Zubarev's nonequilibrium statistical operator method based on the principle of maximum Renyi entropy. In the framework of this approach, we obtain transport equations for the basic set of parameters of the reduced description of nonequilibrium processes in a classical system of interacting particles using Liouville equations with fractional derivatives. For a classical systems of particles in a medium with a fractal structure, we obtain a non-Markovian diffusion equation with fractional spatial derivatives. For a concrete model of the frequency dependence of a memory function, we obtain generalized Kettano-type diffusion equation with the spatial and temporal fractality taken into account. We present a generalization of nonequilibrium thermofield dynamics in Zubarev's nonequilibrium statistical operator method in the framework of Renyi statistics.
Keywords: Renyi entropy, nonequilibrium statistical operator, generalized transport equation
Mots-clés : diffusion equation. 
@article{TMF_2018_194_1_a3,
     author = {P. A. Glushak and B. B. Markiv and M. V. Tokarchuk},
     title = {Zubarev's nonequilibrium statistical operator method in the~generalized statistics of multiparticle systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {71--89},
     publisher = {mathdoc},
     volume = {194},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a3/}
}
TY  - JOUR
AU  - P. A. Glushak
AU  - B. B. Markiv
AU  - M. V. Tokarchuk
TI  - Zubarev's nonequilibrium statistical operator method in the~generalized statistics of multiparticle systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 71
EP  - 89
VL  - 194
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a3/
LA  - ru
ID  - TMF_2018_194_1_a3
ER  - 
%0 Journal Article
%A P. A. Glushak
%A B. B. Markiv
%A M. V. Tokarchuk
%T Zubarev's nonequilibrium statistical operator method in the~generalized statistics of multiparticle systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 71-89
%V 194
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a3/
%G ru
%F TMF_2018_194_1_a3
P. A. Glushak; B. B. Markiv; M. V. Tokarchuk. Zubarev's nonequilibrium statistical operator method in the~generalized statistics of multiparticle systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 1, pp. 71-89. http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a3/