Abstract
We apply the existence theorem for solutions of the equations of motion for infinite systems to study the time evolution of measures on the set of locally finite configurations of particles. The set of allowed initial configurations and the time evolution mappings are shown to be measurable. It is shown that infinite volume limit states of thermodynamic ensembles at low activity or for positive potentials are concentrated on the set of allowed initial configurations and are invariant under the time evolution. The total entropy per unit volume is shown to be constant in time for a large class of states, if the potential satisfies a stability condition.
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On leave from: Department of Mathematics, University of California, Berkeley, California.
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Lanford, O.E. The classical mechanics of one-dimensional systems of infinitely many particles. Commun.Math. Phys. 11, 257–292 (1969). https://doi.org/10.1007/BF01645848
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DOI: https://doi.org/10.1007/BF01645848