Kozlov, V. V.; Treschev, D. V. 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. Cited in 1 ReviewCited in 1 Document 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 Keywords:families of probability measures; shifts of a given measure; rate of the shift; second law of thermodynamics; one-parameter group of diffeomorphisms; weak limit; formula for the limit measure; geodesic flows; Hamiltonian quasi-homogeneous systems × Cite Format Result Cite Review PDF Full Text: DOI References: [1] W. Gibbs, Elementary Principles in Statistical Mechanics Developed with Especial Reference to the Rational Foundation of Thermodynamics, New York (1902). · JFM 33.0708.01 [2] H. Poincare, ”Reflections sur la theorie cinetique des gaz,” J. Phys. Theoret. et Appl., 4e Ser., 5, 369–403 (1906). · JFM 37.0944.02 · doi:10.1051/jphystap:019060050036900 [3] V. V. Kozlov, ”Heat equilibrium according to Gibbs and Poincare,” Dokl. Akad. Nauk, 382, No.5, 602–606 (2002). [4] V. V. Nemytsky and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Moscow (1947). [5] V. V. Kozlov, ”Kinetic of collisionless continuous medium,” Regul. Chaotic Dyn., 6, No.3, 235–251 (2001). · Zbl 1006.82011 · doi:10.1070/RD2001v006n03ABEH000175 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.