Communications in Mathematical Physics

, Volume 129, Issue 3, pp 445–480 | Cite as

Hydrodynamic limit for a system with finite range interactions

  • Fraydoun Rezakhanlou


We study a system of interacting diffusions. The variables present the amount of charge at various sites of a periodic multidimensional lattice. The equilibrium states of the diffusion are canonical Gibbs measures of a given finite range interaction. Under an appropriate scaling of lattice spacing and time, we derive the hydrodynamic limit for the evolution of the macroscopic charge density.


Neural Network Statistical Physic Equilibrium State Complex System Charge Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barbu, V.: Nonlinear semigroups and differential equations in banach spaces. Noordhoff 1976Google Scholar
  2. 2.
    Ellis, R. S.: Entropy, large deviations and statistical mechanics. Grundleheren der Mathematischen Wissenschaften vol.271. Berlin, Heidelberg, New York: Springer 1985Google Scholar
  3. 3.
    Fritz, J.: On the hydrodynamic limit of a Ginzburg-Landau lattice model. Prob. Th. Rel. Fields81, 291–318 (1989)CrossRefGoogle Scholar
  4. 4.
    Guo, M. Z., Papanicoulaou, G. C., Varadhan, S. R. S.: Nonlinear diffusion limit for a system with nearest neighbor interactions. Commun. Math. Phys.118, 31–59 (1988)CrossRefGoogle Scholar
  5. 5.
    Haraux, A.: Nonlinear evolution equations, global behavior of solutions. Lecture Notes in Mathematics, vol.841. Berlin, Heidelberg, New York: Springer 1981Google Scholar
  6. 6.
    Kipnis, C., Olla, S., Varadhan, S. R. S.: Hydrodynamics and large deviations for simple exclusion process. Commun. Pure Appl. Math. (to appear 1989)Google Scholar
  7. 7.
    Ladyženskaja, O. A., Solonnikov, V. A., Ural'ceva, N. N.: Linear and quasilinear equations of parabolic type. Transl. Math. Monographs, vol.23, Providence, RI: Am. Math. Soc. 1968Google Scholar
  8. 8.
    Lifshitz, E. M., Pitaevskii, L. P.: Course on theoretical physics, vol10. Physical kinetics. Oxford: Pergamon Press 1981Google Scholar
  9. 9.
    Olla, S.: Large deviations for Gibbs random fields. Prob. Th. Rel. Fields77, 343–357 (1988)CrossRefGoogle Scholar
  10. 10.
    Preston, C. J.: Random Fields. Lecture Notes in Mathematics, vol.534. Berlin, Heidelberg, New York: Springer 1976Google Scholar
  11. 11.
    Spohn, H.: Equilibrium fluctuations for some stochastic particle systems. In: Fritz, J., Jaffe, A., Szasz, D. (eds.). Statistical physics and dynamical systems. pp. 67–81. Basel-Boston: Birkhäuser (1985)Google Scholar
  12. 12.
    Stroock, D. W.: An introduction to the theory of large deviations. Berlin, Heidelberg, New York: Springer 1984Google Scholar
  13. 13.
    Varadhan, S. R. S.: Asymptotic probabilities and differential equations. Commun. Pure Appl. Math.19, 261–286 (1966)Google Scholar
  14. 14.
    Varadhan, S. R. S.: Large deviations and applications. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol.46, SIAM (1984)Google Scholar
  15. 15.
    Varadhan, S. R. S.: On the derivation of conservation laws for stochastic dynamics, preprintGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Fraydoun Rezakhanlou
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations