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Weak convergence of measures in conservative systems. (English. Russian original) Zbl 1120.37002
J. Math. Sci., New York 128, No. 2, 2791-2797 (2005); translation from Zap. Nauchn. Semin. POMI 300, 194-205 (2003).
Summary: Families of probability measures on the phase space of a dynamical system are considered. These measures are obtained as shifts of a given measure by the phase flow. Sufficient conditions for the existence of the weak convergence of the measures as the rate of the shift tends to infinity are suggested. The existence of such a limit leads to a new interpretation of the second law of thermodynamics.

MSC:
37A17 Homogeneous flows
37A10 Dynamical systems involving one-parameter continuous families of measure-preserving transformations
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53D25 Geodesic flows in symplectic geometry and contact geometry
80A05 Foundations of thermodynamics and heat transfer
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