Abstract
It is shown that a \({\mathbb{Z}}^2 \)-action on a Lebesgue space is intrinsically random (IR) iff it is a Kolmogorov action (K-action). As a consequence we obtain the fact that the \({\mathbb{Z}}^2 \)-action defined by the Lorentz gas is an IR-action and the \({\mathbb{Z}}^2 \)-action defined by the ideal gas is not an IR-action.
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Courbage, M., Kamiński, B. On Intrinsically Random ℤ2-Actions on a Lebesgue Space. Journal of Statistical Physics 112, 421–427 (2003). https://doi.org/10.1023/A:1023600325382
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DOI: https://doi.org/10.1023/A:1023600325382