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Entropy Methods in Hydrodynamic Scaling

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Abstract

Hydrodynamic scalng is a procedure that attempts rigorously to derive large scale behavior of complex interacting systems from laws governing its evolution that are specified at a smaller scale. The procedure involves statistical averaging over the small scales and can be viewed as part of nonequilibrium statistical mechanics.

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References

  1. C. Boldrighini, R. L. Dobrusin and Yu M. Suhov, One-dimensional hard rod cari-catures of hydrodynamics, J. Stat. Phys. 31 (1983), 577–616.

    Article  Google Scholar 

  2. A. DeMasi and E. Presutti, Mathematical Methods for Hydrodynamical Limits, Lecture Notes in Math., 1501, Springer Verlag, Berlin-Heidelberg-New York, 1991.

    Google Scholar 

  3. M. D. Donsker and S. R. S. Varadhan, Large deviations from a hydrodynamic scaling limit, Comm. Pure. Appl. Math. 42 (1989), 243–270.

    Article  MathSciNet  Google Scholar 

  4. R. Esposito, R. Marra and H. T. Yau, Diffusive limit of asymmetric simple exclusion, preprint.

    Google Scholar 

  5. M. Z. Guo, G. C. Papanicolaou and S. R. S. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions, Comm. Math. Phys. 118 (1988), 31–59.

    Article  MathSciNet  Google Scholar 

  6. C. Kipnis, S. Olla and S. R. S. Varadhan, Hydrodynamics and large deviation for simple exclusion process, Comm. Pure Appl. Math. 42 (1989), 115–137.

    Article  MathSciNet  Google Scholar 

  7. C. Kipnis and S. R. S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and application to simple exclusions, Comm. Math. Phys. 104 (1986), 1–19.

    Article  MathSciNet  Google Scholar 

  8. S. Olla, S. R. S. Varadhan and H. T. Yau, Hydrodynamical limit for a Hamiltonian system with weak noise, Comm. Math. Phys. 155 (1993), 523–560.

    Article  MathSciNet  Google Scholar 

  9. J. Quastel, Diffusion of color in simple exclusion process, Comm. Pure Appl. Math. 45 (1992), 623–680.

    Article  MathSciNet  Google Scholar 

  10. F. Rezakhanlou, Hydrodynamical limit for attractive particle systems on z d, Comm. Math. Phys. 140 (1991), 417–448.

    Article  MathSciNet  Google Scholar 

  11. H. Spohn, Large Scale Dynamics of Interacting Particles, Texts and Monographs in Physics, Springer Verlag, Berlin-Heidelberg-New York, 1991.

    Book  Google Scholar 

  12. S. R. S. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions, II, Asymptotic Problems in Probability Theory, in: Stochastic Models and Diffusions on Fractals (K. D. Elworthy and N. Ikeda, eds.), Pitman Res. Notes Math. Ser. 283, 1991, 75–130.

    Google Scholar 

  13. Lin Xu, Hydrodynamics for asymmetric mean zero simple exclusion, Ph.D. thesis, New York University, 1993.

    Google Scholar 

  14. H. T. Yau, Relative entropy and the hydrodynamics of Ginzburg-Landau models, Lett. Math. Phys. 22 (1991), 63–80.

    Article  MathSciNet  Google Scholar 

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© 1995 Birkhäser Verlag, Basel, Switzerland

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Varadhan, S. (1995). Entropy Methods in Hydrodynamic Scaling. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9078-6_15

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  • DOI: https://doi.org/10.1007/978-3-0348-9078-6_15

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9897-3

  • Online ISBN: 978-3-0348-9078-6

  • eBook Packages: Springer Book Archive

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