Global invariants and equilibrium states in lattice gases |
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Authors: | D. Bernardin |
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Affiliation: | (1) Lemta U.A. CNRS 875, B.P. 160, 54504 Vandoeuvre-lès-Nancy Cedex, France |
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Abstract: | It is now well known that, in addition to the physical conserved quantities, lattice gases also have other unphysical ones related to the discretization of their phase space. From an abstract point of view a lattice gas can be considered like a full discrete Markov processL and these spurious conserved quantities yield the existence of a nonspatially homogeneous equilibrium state forLk. We show that a particular set of these conserved quantities is of special interest: Its elements will be called regular. These regular invariants are simply built from the local ones and their projection on each node is always a locally conserved quantity. Moreover, for most models they are one-to-one related to the Gibbs states ofLk which remain factorized. It turns out that all the classical known spurious invariants are regular and one can exhibit simple conditions to build models with only regular invariants. For the latter it is then justified to determine the transport coefficients of the locally conserved densities with the Green-Kubo procedure. |
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Keywords: | Lattice gases cellular automata global invariants invariants in discrete stochastic processes equilibrium states in lattice gases |
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