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Ergodic properties of infinite systems. (English) Zbl 0316.28008

Dyn. Syst., Theor. Appl., Battelle Seattle 1974 Renc., Lect. Notes Phys. 38, 112-143 (1975).
Macroscopic systems are successfully modeled in statistical mechanics, at least in equilibrium, by infinite systems. We discuss the ergodic theoretic structure of such systems and present results on the ergodic properties of some simple model systems. We argue that these properties, suitably refined by the inclusion of space translations and other structure, are important for an understanding of the nonequilibrium properties of macroscopic systems. It is argued in particular that the time evolutions of infinite systems, even if they lack a local mixing “mechanism”, should be very strongly mixing, whereas strong ergodic properties under the group of space-time translations do reflect the existence of a local stochastic mechanism.
Reviewer: S. Goldstein

MSC:

37A60 Dynamical aspects of statistical mechanics
82B05 Classical equilibrium statistical mechanics (general)
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
28D10 One-parameter continuous families of measure-preserving transformations
37A10 Dynamical systems involving one-parameter continuous families of measure-preserving transformations
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