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References
Arnold V.I. (1978), Mathematical methods of Classical Mechanics. Springer-Verlag, New-York, 462p.
Boldrighini C., Dobrushin R.L., Suhov Yu.M. (1983), One-dimensional hard rod caricature of hydrodynamics. J. Stat. Phys., 31, No. 3, 577–615.
Chulaevsky F. A. (1983), The inverse problem method of scattering theory in statistical physics. Funct. Anal. and its Appl., 17, No 1, 53–62.
Dobrushin R. L. (1956), On Poisson's law for distribution of particles in space. Ukrain. Math. J., 8, No 2, 127–134.
Dobrushin R. L., Fritz J. (1977), Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-rod interaction. Comm. Math. Phys., 55, no 3, 275–292.
Dobrushin R. L., Sinai Ya. G., Suhov Yu. M. (1985), Dynamical systems in statistical mechanics. In Modern Mathematical Problems, Dynamical Systems, 2 (in Russian). 235–284, In Encyclopaedia of Math. Sci., Dynamical Systems, 2, (1989) (Engl. transl.), Springer-Verlag, Berlin.
Dobrushin R., Sokolovskii F. (1991), Higher order hydrodinamical equations for a system of independent random walks. In Random walks, Brownian motion and Interacting Particle Systems, A Festschrift in Honor of Frank Spitzer, Birkhauser, Boston-Basel-Berlin, 231–254.
Dobrushin R. L., Suhov Yu. M. (1979), Time asymptotics for some degenerate models of infinite particles evolution system. In Modern Mathematical Problems (in Russian) 14, 148–254.
Doob J. (1953), Stochastic Processes. John Wiley & Sons, New-York, Chapman & Hall, London, 654p.
Fritz J., Dobrushin R. L. (1977), Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction. Comm. Math. Phys., 57, No 1, 67–81.
Gallavotti G., Lanford O. E., Lebowitz J. L. (1972), Thermodynamic limit of the time dependent correlation functions for one-dimensional systems. J. Math. Phys., 13, No. 11, 2898–2905.
Georgii H. O. (1958), Gibbsian Measures and Phase Transition. Walter de Gruyter, Berlin-New York, 525p.
Gurevich B. M., Suhov Yu. M. (1976–1982), Stationary solutions of the Bogolubov hierarchy equations in classical statistical mechanics, 1–4. Comm. Math. Phys., 49 (1976), No. 1, 69–96, 56 (1977), No. 1, 81–96, 56 (1977), No. 3, 225–236, 84 (1972), No. 4, 333–376.
Lanford O. E. (1968–1969), The classical mechanics of one-dimensional systems of infinetely many particles, 1. An existence theorem. Comm. Math. Phys., 9, No. 3, 176–191, 2. Kinetic theory. bf 11, No. 4, 257–292.
Morrey C. B. (1955), On the derivation of the equations of hydrodynamics from statistical mechanics. Comm. Pure Appl. Math., 8, No. 2, 279–326.
Presutti E., Pulverenti M., Tirozzi B. (1976), Time evolution of infinite classical systems with singular, long-range, two-body interaction. Comm. Math. Phys., 47, No. 1, 81–95.
Sinai Ya. G. (1982), Theory of phase-transition: rigorious results. Pergamon Press, Oxford-New York, 150p.
Sinai Yu. G., Suhov Yu. M. (1974), On the existence theorem for the solutions of Bogolubov class of equations, Theor. Math. Phys., 19, 344–363.
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Dobrushin, R.L. (1993). On the way to the mathematical foundations of statistical mechanics. In: Statistical Mechanics and Fractals. Lecture Notes in Mathematics, vol 1567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074239
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DOI: https://doi.org/10.1007/BFb0074239
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