Syllabus
* Macroscopic irreversibility
Boltzmann equation for rarefied gas; H-theorem; Zermelo-Poincare and Loschmidt paradoxes; Kac model; macroscopic autonomy; Onsager-Machlup symmetry and thermodynamic arrow of time.
* Stochastic dynamics
Formal construction of reduced dynamics from mechanical equations; detailed balance and the time-reversal symmetry; Markov jump processes; Kolmogorov generator and its spectral properties; path distribution.
* Systems coupled to heat bath
Relaxation and thermodynamic processes; entropy production; minimal work principle, statistical distributions for work and heat; Jarzynski equation, quasistatic ("adiabatic") limit; fluctuation-dissipation theorem; Onsager regression hypothesis.
* Non-equilibrium stochastic processes
Systems interacting with more baths; local detailed balance principle; entropy production as a measure of the time-reversal symmetry breaking; thermodynamic formalism for stationary fluctuations; Gallavotti-Cohen fluctuation symmetry; perturbative calculation of current cumulants.
* Thermodynamics of weakly non-equilibrium systems
Green-Kubo linear response relations; Onsager reciprocities; McLennan stationary ensemble; minimum entropy production principle; time-symmetric fluctuations.
* Diffusion processes
Diffusion limit of random walk; continuous Markov processes; overdamped and underdamped diffusion, Johnson-Nyquist noise; Onsager-Machlup theory of dynamical fluctuations.
Annotation
Basic ideas and recent trends in non-equilibrium statistical mechanics. We discuss the irreversibility of macroscopic dynamics in relation to the microscopic reversibility and the essential role played by the detailed balance and its local generalization for understanding the behavior of open thermodynamic systems out of equilibrium. We derive some symmetry relations for dynamical fluctuations and basic statistical properties of non- equilibrium processes.
For the 1st and 2nd year of study and for doctoral students.