Abstract
For every Gibbs measure on the one dimensional lattice Z with translation-invariant potential of finite range, an exchange rate for one-dimensional lattice gas which satisfy both the detailed balance condition relative to the Gibbs measure and the gradient condition is constructed.
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REFERENCES
T. Funaki, K. Handa, and K. Uchiyama, Hydrodynamic limit of one-dimensional exclusion process with speed change, Ann. Probab. 19:245–265 (1991).
T. Funaki, K. Uchiyama, and H. T. Yau, Hydrodynamic limit for lattice gas reversible under Bernoulli measures, in Nonlinear Stochastic PDE's: Hydrodynamic Limit and Burgers' Turbulaence, IMA Volume 77 (Springer, 1995), pp. 1–40.
S. L. Lu and H. T. Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Commun. Math. Phys. 156:399–433 (1992).
H. Spohn, Large Scale Dynamics of Interacting Particles (Springer, 1991).
S. R. S. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions-II, in Asymptotic Problems in Probability Theory: Stochastic Models and Diffusions on Fractals (Longman, 1993), pp. 75–128.
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Nagahata, Y. The Gradient Condition for One-Dimensional Symmetric Exclusion Processes. Journal of Statistical Physics 91, 587–602 (1998). https://doi.org/10.1023/A:1023025510497
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DOI: https://doi.org/10.1023/A:1023025510497