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TMF, 1972, Volume 11, Number 2, Pages 248–258 (Mi tmf2857)  

This article is cited in 13 scientific papers (total in 15 papers)

Construction of dynamics in one-dimensional systems of statistical mechanics

Ya. G. Sinai

Abstract: It is well known that in one-dimensional systems the microcanonical, small canonical, and grand canonical distributions have the same thermodynamic limit. This limit can be regarded as a measure on the phase space of an infinite system of particles. Under the assumption that the binary interaction potential has compaet support, it is shown that one can find a one- parametric group of transformations in the phase space that preserve this measure and are related in a natural manner to the infinite system of Hamiltonian equations that describe the motion of the particles. This result has been previously proved by Lanford under the assumption that the potential has bounded modulus and finite range.

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English version:
Theoretical and Mathematical Physics, 1972, 11:2, 487–494

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Received: 09.07.1971

Citation: Ya. G. Sinai, “Construction of dynamics in one-dimensional systems of statistical mechanics”, TMF, 11:2 (1972), 248–258; Theoret. and Math. Phys., 11:2 (1972), 487–494

Citation in format AMSBIB
\by Ya.~G.~Sinai
\paper Construction of dynamics in one-dimensional systems of statistical mechanics
\jour TMF
\yr 1972
\vol 11
\issue 2
\pages 248--258
\jour Theoret. and Math. Phys.
\yr 1972
\vol 11
\issue 2
\pages 487--494

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    This publication is cited in the following articles:
    1. A. N. Zemlyakov, “Postroenie dinamiki v odnomernykh sistemakh statisticheskoi fiziki v sluchae nefinitnykh potentsialov”, UMN, 28:1(169) (1973), 239–240  mathnet  mathscinet
    2. B. M. Gurevich, Ya. G. Sinai, Yu. M. Sukhov, “On invariant measures of dynamical systems of one-dimensional statistical mechanics”, Russian Math. Surveys, 28:5 (1973), 49–86  mathnet  crossref  mathscinet  zmath
    3. Ya. G. Sinai, Yu. M. Sukhov, “Existence theorem for solutions of the Bogolyubov equations”, Theoret. and Math. Phys., 19:3 (1974), 560–573  mathnet  crossref  mathscinet  zmath
    4. D. Ya. Petrina, “Mathematical description of the evolution of infinite systems of classical statistical physics. I. Locally perturbed one-dimensional systems”, Theoret. and Math. Phys., 38:2 (1979), 153–166  mathnet  crossref  mathscinet
    5. P. V. Malyshev, “Mathematical description of the evolution of an infinite classical system”, Theoret. and Math. Phys., 44:1 (1980), 603–611  mathnet  crossref  mathscinet  isi
    6. B. I. Shubov, “On the unique solvability of the Cauchy problem for the equations of motion of discrete analogs of multidimensional chiral fields taking values on compact symmetric spaces”, Theoret. and Math. Phys., 49:2 (1981), 966–974  mathnet  crossref  mathscinet  zmath  isi
    7. D. Ya. Petrina, V. I. Gerasimenko, “A mathematical description of the evolution of the state of infinite systems of classical statistical mechanics”, Russian Math. Surveys, 38:5 (1983), 1–61  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. V. A. Chulaevskii, “Stationary measures of integrable systems in statistical physics”, Russian Math. Surveys, 38:6 (1983), 115–116  mathnet  crossref  mathscinet  adsnasa  isi
    9. V. A. Chulaevskii, “Inverse scattering method in statistical physics”, Funct. Anal. Appl., 17:1 (1983), 40–47  mathnet  crossref  mathscinet  isi
    10. M. R. Soloveichik, “Ergodic properties of systems with an external potential in classical statistical mechanics”, Math. USSR-Izv., 34:1 (1990), 181–200  mathnet  crossref  mathscinet  zmath
    11. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    12. B. M. Gurevich, “Dynamical aspects of statistical physics in Dobrushin's works”, Russian Math. Surveys, 52:2 (1997), 257–264  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    13. V. A. Malyshev, “Analytic Dynamics of a One-Dimensional System of Particles with Strong Interaction”, Math. Notes, 92:2 (2012), 237–248  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    14. A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. M. V. Tantsiura, “On strong solutions to countable systems of SDEs with interaction and non-Lipschitz drift”, Theory Stoch. Process., 21(37):1 (2016), 91–101  mathnet  mathscinet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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