#That a longstanding quasi-stationary state (QSS) was expected in LONG-range interacting Hamiltonian systems (one of the core problems of statistical mechanics).
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In mathematical physics, Liouville made two fundamental contributions: the Sturm–Liouville theory, which was joint work with Charles François Sturm, and is now a standard procedure to solve certain types of integral equations by developing into eigenfunctions, and the fact (also known as Liouville's theorem) that time evolution is measure preserving for a Hamiltonian system.