Abstract:
The paper is devoted to the problem of convergence to the equilibrium state in the motion of infinite systems of classical particles. Two models of the motion are considered: free motion of point particles in Euclidean space Rν, ν⩾1, and motion of solid rods on the line R1. The paper contains new results obtained by the authors and also a survey of previous results in this direction.
K. Boldrigini took part in the work on the paper.
Citation:
R. L. Dobrushin, Yu. M. Sukhov, “Asymptotic behavior for some degenerate models of the time evolution of systems with an infinite number of particles”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 14, VINITI, Moscow, 1979, 147–254; J. Soviet Math., 16:4 (1981), 1277–1340
\Bibitem{DobSuk79}
\by R.~L.~Dobrushin, Yu.~M.~Sukhov
\paper Asymptotic behavior for some degenerate models of the time evolution of systems with an infinite number of particles
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat.
\yr 1979
\vol 14
\pages 147--254
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd40}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=570796}
\zmath{https://zbmath.org/?q=an:0462.60097|0424.60096}
\transl
\jour J. Soviet Math.
\yr 1981
\vol 16
\issue 4
\pages 1277--1340
\crossref{https://doi.org/10.1007/BF01084894}
Linking options:
https://www.mathnet.ru/eng/intd40
https://www.mathnet.ru/eng/intd/v14/p147
This publication is cited in the following 17 articles:
V. V. Ryazanov, “Obtaining the thermodynamic relations for the Gibbs ensemble using the maximum entropy method”, Theoret. and Math. Phys., 194:3 (2018), 390–403
T. V. Dudnikova, A. I. Komech, “On a two-temperature problem for Klein–Gordon equation”, Theory Probab. Appl., 50:4 (2006), 582–611
B. M. Gurevich, “Dynamical aspects of statistical physics in Dobrushin's works”, Russian Math. Surveys, 52:2 (1997), 257–264
E. A. Pechersky, Yu. M. Sukhov, “Dobrushin's ideas in the theory of queuing networks”, Russian Math. Surveys, 52:2 (1997), 265–269
V. I. Gerasimenko, “Solutions of Bogolyubov equations for one-dimensional system of hard spheres”, Theoret. and Math. Phys., 91:1 (1992), 410–417
N. E. Ratanov, Yu. M. Sukhov, “Invariant states for time dynamics of one-dimensional lattice quantum fermi systems”, Theoret. and Math. Phys., 88:2 (1991), 849–858
D. Ya. Petrina, V. I. Gerasimenko, “Mathematical problems of statistical mechanics of a system of elastic balls”, Russian Math. Surveys, 45:3 (1990), 153–211
Mustafid, “The law of small numbers and the limit theorem for symmetric statistics with mixing conditions”, Hiroshima Math. J., 20:1 (1990)
E. V. Gusev, “Convergence of model Heisenberg dynamics”, Theoret. and Math. Phys., 77:1 (1988), 1010–1018
Hans Zessin, “On the asymptotic behaviour of the free gas and its fluctuations in the hydrodynamical limit”, Probab. Th. Rel. Fields, 77:4 (1988), 605
Yu. M. Sukhov, A. G. Shukhov, “Convergence to a stationary state for one-dimensional lattice quantum models of hard rods”, Theoret. and Math. Phys., 73:1 (1987), 1104–1115
Hermann Rost, Lecture Notes in Mathematics, 1215, Lectures in Probability and Statistics, 1986, 129
E. Presutti, Ya. G. Sinai, M. R. Soloviechik, Statistical Physics and Dynamical Systems, 1985, 253
Yu. M. Sukhov, “Linear boson models of time evolution in quantum statistical mechanics”, Math. USSR-Izv., 24:1 (1985), 151–182
Yu. M. Sukhov, “Convergence to equilibrium for a free Fermi gas”, Theoret. and Math. Phys., 55:2 (1983), 503–508
Yu. M. Sukhov, “Convergence to a Poisson distribution for certain models of particle motion”, Math. USSR-Izv., 20:1 (1983), 137–155
Yu. M. Sukhov, “Convergence to an equilibrium state for a one-dimensional quantum system of hard rods”, Math. USSR-Izv., 21:3 (1983), 547–583
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