Nonequilibrium and Irreversibility

Equilibrium.- Many particles systems: kinematics, timing.- Birth of kinetic theory.- Heat theorem and Ergodic hypothesis.- Least action and heat theorem.- Heat Theorem and Ensembles.- Boltzmann s equation, entropy, Loschmidt s paradox.- Conclusion.- Stationary Nonequilibrium.- Thermostats and infinite models.- Finite thermostats.- Examples of nonequilibrium problems.- Initial data.- Finite or infinite thermostats? Equivalence?.- SRB distributions.- Chaotic Hypothesis.- Phase space contraction in continuous time.- Phase space contraction in timed observations.- Conclusions.- Discrete phase space.- Recurrence.- Hyperbolicity: stable & unstable manifolds.- Geometric aspects of hyperbolicity. Rectangles.- Symbolic dynamics and chaos.- Examples of hyperbolic symbolic dynamics.- Coarse graining and discrete phase space.- Coarse cells, phase space points and simulations.- The SRB distribution: its physical meaning.- Other stationary distributions.- Phase space cells and entropy.- Counting phase space cells out of equilibrium.- kB logN entropy or Lyapunov function?.- Fluctuations.- SRB potentials.- Chaos and Markov processes.- Symmetries and time reversal.- Pairing rule and Axiom C.- Large deviations.- Time reversal and fluctuation theorem.- Fluctuation patterns.- Onsager reciprocity, Green-Kubo formula, fluctuation theorem.- Local fluctuations: an example.- Local fluctuations: generalities.- Quantum systems, thermostats and non equilibrium.- Quantum adiabatic approximation and alternatives.- Applications.- Equivalent thermostats.- Granular materials and friction.- Neglecting granular friction: the relevant time scales.- Simulations for granular materials.- Fluids.- Developed turbulence.- Intermittency.- Stochastic evolutions.- Very large fluctuations.- Thermometry.- Processes time scale and irreversibility.- Historical comments.- Proof of the second fundamental theorem.- Collision analysis and equipartition.- Dense orbits: an example.- Clausius version of recurrence and periodicity.- Clausius mechanical proof of the heat theorem.- Priority discussion of Boltzmann (vs. Clausius ).- Priority discussion: Clausius reply.- ...