Brief abstract: Starting from the Kac ring model and ending with the lattice random Lorentz gas (mirrors model), this series of lectures will explain a strategy that allows a　rigorous derivation of the evolution laws of macroscopic quantities in the context　of non-ergodic Hamiltonian dynamics.

Plan of the lectures:
Lecture 1 : Introduction
Lecture 2 : The Kac's ring model
Lecture 3 : The rings model
Lecture 4 : Derivation of Fick's law for the current of particles in lattice random Lorentz gases out of equilibrium
Lecture 5 : Perspectives on the general lattice random Lorentz gas

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