Abstract
The large scale behavior of FHP-type cellular automata is investigated in the presence of some additional random effects. It is shown that every translationinvariant stationary state of the modified model is a superposition of product measures. By means of the entropy argument of Yau and of Olla, Varadhan, and Yau, the macroscopic (Euler-type) equations governing the hydrodynamic behavior of FHP automata are also derived.
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References
U. Frish, B. Hasslacher, and Y. Pomeau, Lattice gas automata for Navier-Stokes equation,Phys. Rev. Lett. 56:1505 (1986).
J. Fritz, On the stationary measures of anharmonic systems in the presence of a small thermal noise,J. Stat. Phys. 44:25–47 (1986).
J. Fritz, Hydrodynamics of FHP automata via OYV and ergodicity, Notes, Rutgers University (1990).
J. Fritz, T. Funaki, and J. L. Lebowitz, Stationary states of random Hamiltonian systems,Probab. Th. Rel. Fields 99: 211–236 (1994). Preprint, MKI Budapest (1992).
G. Gallavotti and M. Verboven, On the classical KMS condion,Nuovo Cimento 28B:274–286 (1976).
M. Z. Guo, G. Papanicolau, and S. R. S. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions,Commun. Math. Phys. 118:31–53 (1988).
J. Hardy, O. dePazzis, and Y. Pomeau, Molecular dynamics of classical lattice gas: Transport properties and time correlation functions,Phys. Rev. A 13:1949 (1976).
R. Holley, Free energy in a Markovian model of a lattice spin system,Commun. Math. Phys. 23:87–99 (1971).
S. Olla and S. R. S. Varadhan, Scaling limit for interacting Ornstein-Uhlenbeck processes,Commun. Math. Phys. 135:355–378 (1991).
S. Olla, S. R. S. Varadhan, and H. T. Yau, Derivation of Euler equations from Hamiltonian dynamics with weak noiseCommun. Math. Phys. 155:523–560 (1993).
J. Smoller,Shock Waves and Reaction-Diffusion Equations (Springer-Verlag, New York, 1983).
H. Spohn,Large Scale Dynamics of Interacting Particles (Springer-Verlag, New York, 1991).
H. T. Yau, Relative entropy and hydrodynamics of Ginzburg-Landau models,Lett. Math. Phys. 22:63 (1991).
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Dedicated to Oliver Penrose on the occasion of his 65th birthday.
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Fritz, J. Stationary states and hydrodynamics of FHP cellular automata. J Stat Phys 77, 53–76 (1994). https://doi.org/10.1007/BF02186832
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DOI: https://doi.org/10.1007/BF02186832