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Weak convergence of solutions of the Liouville equation for nonlinear Hamiltonian systems. (English) Zbl 1178.37050
Theor. Math. Phys. 134, No. 3, 339-350 (2003); translation from Teor. Mat. Fiz. 134, No. 3, 388-400 (2003).
Summary: We suggest sufficient conditions for the existence of weak limits of solutions of the Liouville equation as time increases indefinitely. The presence of the weak limit of the probability distribution density leads to a new interpretation of the second law of thermodynamics for entropy increase.

MSC:
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
70H05 Hamilton’s equations
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
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