Letters in Mathematical Physics

, Volume 45, Issue 4, pp 323–330 | Cite as

On Thermodynamic Limits of Entropy Densities

  • Hajime Moriya
  • Aernout Van Enter


We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.

entropy density local Gibbs state 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Araki, H.: On KMS states of a C*-dynamical system, Lecture Notes in Math.650, Springer-Verlag, New York, 1978, pp. 66-84.Google Scholar
  2. 2.
    Araki, H.: Toukeibuturi no suuri, Iwanami in Japanese 1994.Google Scholar
  3. 3.
    Bratteli, O. and Robinson, D. W.: Operator Algebras and Quantum Statistical Mechanics II, 2nd edn, Springer-Verlag, New York, 1997.Google Scholar
  4. 4.
    Haag, R., Hugenholtz, N. M. and Winnink, M.: On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys. 5(1967), 215-236.Google Scholar
  5. 5.
    Israel, R. B.: Convexity in the Theory of Lattice Gases, Princeton University Press, 1979.Google Scholar
  6. 6.
    Moriya, H.: Entropy density for one-dimensional quantum lattice systems, Rev. Math. Phys. 9(1997), 361-369.Google Scholar
  7. 7.
    Sakai, S.: On one-parameter subgroups of *-automorphisms on operator algebras and the corresponding unbounded derivations, Amer. J. Math. 98(1976), 427-440.Google Scholar
  8. 8.
    Simon, B.: The Statistical Mechanics of Lattice Gases, Princeton University Press, 1993.Google Scholar
  9. 9.
    Martin-Löf, A.: Statistical Mechanics and the Foundation of Thermodynamics, Lecture Notes in Phys. 101, Springer-Verlag, New York, 1979.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Hajime Moriya
    • 1
  • Aernout Van Enter
    • 2
  1. 1.Research Institute Mathematical ScienceKyoto UniversityKyotoJapan
  2. 2.Institute for Theoretical Physics, RUGGroningenThe Netherlands

Personalised recommendations