Geodesic
Gibbs random fields invariant under infinite-particle Hamiltonian dinamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 3, pp. 424-459

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The Liouville operator for an infinite-particle Hamiltoniaa dynamics corresponding to interaction potential $U$ is used to introduce the concept of a locally weakly invariant measure on the phase space and to show that if a Gibbs measure with potential of general form is locally weakly invariant then its Hamiltonian is asymptotically an additive integral of the motion of the particles with the interaction $U$. 
@article{TMF_1992_90_3_a7,
     author = {B. M. Gurevich},
     title = {Gibbs random fields invariant under infinite-particle {Hamiltonian} dinamics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {424--459},
     publisher = {mathdoc},
     volume = {90},
     number = {3},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_90_3_a7/}
}
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B. M. Gurevich. Gibbs random fields invariant under infinite-particle Hamiltonian dinamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 90 (1992) no. 3, pp. 424-459. http://geodesic.mathdoc.fr/item/TMF_1992_90_3_a7/