Communications in Mathematical Physics

, Volume 5, Issue 4, pp 288–300 | Cite as

Mean entropy of states in classical statistical mechanics

  • Derek W. Robinson
  • David Ruelle


The equilibrium states for an infinite system of classical mechanics may be represented by states over AbelianC* algebras. We consider here continuous and lattice systems and define a mean entropy for their states. The properties of this mean entropy are investigated: linearity, upper semi-continuity, integral representations. In the lattice case, it is found that our mean entropy coincides with theKolmogorov-Sinai invariant of ergodic theory.


Entropy Neural Network Statistical Physic Equilibrium State Complex System 
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  1. 1.
    Billingsley, P.: Ergodic theory and information. New York: John Wiley 1965.Google Scholar
  2. 2.
    Choquet, G., andP. A. Meyer: Ann. Inst. Fourier13, 139 (1963).Google Scholar
  3. 3.
    Doplicher, S., D. Kastler, andD. W. Robinson: Commun. Math. Phys.3, 1 (1966).Google Scholar
  4. 4.
    Jacobs, K.: Lecture notes on ergodic theory. Aarhus Universitet (1962–1963).Google Scholar
  5. 5.
    Kastler, D., andD. W. Robinson: Commun. Math. Phys.3, 151 (1966).Google Scholar
  6. 6.
    Lanford, O., andD. Ruelle: J. Math. Phys. (to appear).Google Scholar
  7. 7.
    Robinson, D. W., andD. Ruelle: Ann. Inst. Poincaré (to appear).Google Scholar
  8. 8.
    -- Unpublished.Google Scholar
  9. 9.
    Rokhlin, V. A.: Am. Math. Soc. Transl.49, 171 (1966).Google Scholar
  10. 10.
    Ruelle, D.: Lecture notes of the Summer School of Theoretical Physics, Cargèse, Corsica (1965), and Commun. Math. Phys.3, 133 (1966).Google Scholar
  11. 11.
    -- J. Math. Phys. (to appear).Google Scholar
  12. 12.
    Segal, I. E.: Duke Math. J.18, 221 (1951).Google Scholar
  13. 13.
    Yang, C. N., andT. D. Lee: Phys. Rev.87, 404, 410 (1952).Google Scholar

Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • Derek W. Robinson
    • 1
  • David Ruelle
    • 2
  1. 1.CERNGeneva
  2. 2.I.H.E.S., Bures-sur-YvetteFrance

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