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On the problem of the mathematical foundation of the Gibbs postulate ie classical statistical mechanics

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References

  1. Lanford,O.E.,III, Classical Mechanics of One-Dimensional Systems of Infinitely Many Particles, I,II. Commun.Math.Phys.9 (1969), 169–181; 11(1969), 257–292.

    Google Scholar 

  2. Gurevich, B. M., Sinai, Ya.G., Suhov Yu.M., On Invariant Yeasures for Dynamical Systems of One-Dimensional Statistical Mechanics. Uspekhi natem.Nauk-(Russian) 28:5 (1973), 45–82.

    Google Scholar 

  3. Lanford,O.E.,III, Time Evolution of Large Classical Systems. Lect. Notes in Phys. 38 (1975), 1–97.

    Google Scholar 

  4. Lenard,A., States of Classical Statistical Mechanical System of Infinitely 1Aany Particles,I,II. Arch.Rational Mech.Anal. 59:3 (1975), 219–239; 241–256.

    Google Scholar 

  5. Kozlov,O.K., Gibbs'Description of Random Point Fields, Teorija Veroj atn.Primen. (Russian) 21 (1976), 348–365.

    Google Scholar 

  6. Dobrushin,R.L., Fritz,J., a) Non-Equilibrium Dynamics of One-Dimensional Infinite Particle Systems with a Hard-Core Interaction, Commun.Math.Phys.(to appear); b) Non-Equilibrium Dynamics of Two-Dimensional Infinite Particle System with a Singular Interaction, Commun.Math.Phys.(to appear).

    Google Scholar 

  7. Sinai, Ya.G., Construction of Dynamics for One-Dimensional Systems of Statistical Mechanics, Teor.Metem.Fizika (Russian) 11:2 (1972), 248–258; Presutti,E., Pulvirenti,E., Tirozzi,B., Time Evolution of Infinite Classical Systems with Singular, Long Range, Two Body Interactions. Commun.Math.Phys.47(1976), 81.

    Google Scholar 

  8. Gallavotti,G., Lanford,O.E.,III, Lebowitz,J.L., Thermodynamic Limit of Time-Dependent Correlation Functions for One Dimensional Systems. J.Math.Phys.,11 (1972), 2898–2905; Sinai,Ya.G., Suhov,Yu.M., On the Existence Theorem for the Bogoliubov Hierarchy Equations. Teor.Yatem.Fiziks (Russian), 19:3(1974), 344–363.

    Google Scholar 

  9. Gureyich,B.M., SuhoV,Yu.M., Stationary Solutions of the Bogoliubov Hierarchy Equations in Classical Statistical Yechanics,I,II. Commun.Math.Phys.49 (1976), 63–96; 54(1977), 81–96; Part III. Commun. Math.Phys.(to appear); Part IV: in preparation.

    Google Scholar 

  10. Gurevich,B.M., Suhoy,Yu.M., Time Evolution of Gibbs States, to appear.

    Google Scholar 

  11. Dobrushin,R.L., On the Poisson Law for the Particle Distribution in a Space. Ukr.Yatem.Žurn.(Russian) 8:2 (1956), 127–134.

    Google Scholar 

  12. Volkovyssky,K.L., Sinai,Ya.G., a) Ergodic Properties of the Ideal Gas with Infinitely Yany Degrees of Freedom. Funkz,Anal.Pril.(Russian) 5:4 (1971), 19–21; b) Ergodic Properties of the Gas of One-Dimensional Hard Balls with Infinitely Many Degrees of Freedom.Funkz.Anal.Pril. (Russian) 6:1 (1972), 41–50; Aizenman,M., Goldstein,S.,Lebowitz,J.L., Ergodic Properties of an Infinite One Dimensional Hard-Rod System. Commun.math.Phys.39(1974), 289–304.

    Google Scholar 

  13. Kerstan,J., Matthes,K., Mecke,J., Unbegrenzt Teilbare Punktprozesse. Berlin: Akademie-Ferlag 1974.

    Google Scholar 

  14. Dobrushin,,R.L., Suhov Yu.M., Dynamical Systems of Statistical Mechanics, to appear in.: 1Todern Problems of Mathematics (Russian). Moscow: VINITI-Edition 1978.

    Google Scholar 

  15. Rosenblatt, M., A Central Limit Theorem and a Strong Mixing Condition, Proc.Nat.Aced.Sci., USA 42:1 (1956), 43–47.

    Google Scholar 

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G. Dell'Antonio S. Doplicher G. Jona-Lasinio

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© 1978 Springer-Verlag

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Dobrushin, R.L., Suhov, Y.M. (1978). On the problem of the mathematical foundation of the Gibbs postulate ie classical statistical mechanics. In: Dell'Antonio, G., Doplicher, S., Jona-Lasinio, G. (eds) Mathematical Problems in Theoretical Physics. Lecture Notes in Physics, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08853-9_27

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  • DOI: https://doi.org/10.1007/3-540-08853-9_27

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