Geodesic
Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 388-400

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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.
Keywords: Hamiltonian system, weak convergence, entropy.
Mots-clés : Liouville equation 
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     author = {V. V. Kozlov and D. V. Treschev},
     title = {Weak {Convergence} of {Solutions} of the {Liouville} {Equation} for {Nonlinear} {Hamiltonian} {Systems}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_3_a5/}
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V. V. Kozlov; D. V. Treschev. Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 388-400. http://geodesic.mathdoc.fr/item/TMF_2003_134_3_a5/