## Statistical mechanics and microscopic chaos

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Units : Physics of Complex Systems and Statistical Mechanics | ULB492

Ergodic and spectral properties, analysis of the Liouville and Frobenius-Perron operators describing the time evolution of probability densities. Relationships between the transport properties and the characteristic quantities of microscopic chaos (Lyapunov exponents, fractal dimensions, and Pollicott-Ruelle resonances). Liouvillian description of hydrodynamic modes. Effects of longe-range interactions. Ab initio derivation of nonequilibrium thermodynamics and entropy production. Fluctuation and nonequilibrium work theorems. Kolmogorov-Sinai entropy per unit time of the histories of a system. Entropy per unit time of the reversal histories.

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