Abstract
We investigate a new interpretation for the Navier-Stokes corrections to the hydrodynamic equation of asymmetric interacting particle systems. We consider a system that starts from a measure associated with a profile that is constant along the drift direction. We show that under diffusive scaling the macroscopic behavior of the process is described by a nonlinear parabolic equation whose diffusion coefficient coincides with the diffusion coefficient of the hydrodynamic equation of the symmetric version of the process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. L. Dobrushin, Caricature of hydrodynamics,IXth International Congress on Mathematical Physics, B. Simon, A. Truman, and I. M. Davies, eds. (Adam Hilger, Bristol, 1989), pp. 117–132.
R. Esposito and R. Marra, On the derivation of the incompressible Navier-Stokes equation for Hamiltonian particle systems,J. Stat. Phys. 74:981–1004 (1993).
R. Esposito, R. Marra, and H. T. Yau, Diffusive limit of asymmetric simple exclusion,Rev. Math. Phys. 6:1233–1267 (1994).
R. Esposito, R. Marra, and H. T. Yau, Navier-Stokes equations for stochastic lattice gases, preprint (1996).
C. Kipnis and C. Landim, Hydrodynamic limit of interacting particle systems, preprint (1995).
C. Landim, Conservation of local equilibrium for asymmetric attractive particle systems on ∔d,Ann. Prob. 21:1782–1808 (1993).
C. Landim, S. Olla, and H. T. Yau, First order correction for the hydrodynamic limit of asymmetric simple exclusion processes in dimensiond≥3, to appear inCommun. Pure Appl. Math. (1997).
C. Landim, S. Olla, and H. T. Yau, Some properties of the diffusion coefficient for asymmetric simple exclusion processes,Ann. Prob. 24:1779–1807 (1996).
C. Landim and H. T. Yau, Fluctuation-dissipation equation of asymmetric simple exclusion processes, to appear inProbab. Th. Rel. Fields (1997).
J. Quastel and H. T. Yau, Lattice gases, large deviations and the incompressible Navier-Stokes equations, preprint (1996).
F. Rezakhanlou, Hydrodynamic limit for attractive particle systems onZ d,Commun. Math. Phys. 140:417–448 (1990).
H. T. Yau, Relative entropy and hydrodynamics of Ginzburg-Landau models,Lett. Math. Phys. 22:63–80 (1991).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Benois, O., Koukkous, A. & Landim, C. Diffusive behavior of asymmetric zero-range processes. J Stat Phys 87, 577–591 (1997). https://doi.org/10.1007/BF02181237
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02181237