Syllabus

• Thermodynamic potentials: Gibbs free energy; per molecule and per unit volume thermodynamic potentials.

• First order phase transitions: experimental observations; thermodynamic phases; free energy per unit volume; conditions for phase separation; local and global stability of a thermodynamic phase; graphical representation.

• Molecular interactions: hard-core repulsion; Van der Waals attraction; induced dipole; electronic and dipole polarizability; estimations of Van der Waals attraction for simple molecules; Lennard-Jones potential.

• Phase coexistence; common tangent construction; phase diagrams; spinodal and binodal lines; critical temperature; Clausius-Clapeyron equation.

• Van der Waals gas: free energy; pressure; spinodal; critical point; estimations of critical temperature; approximation of binodal far from the critical point.

• Van der Waals gas near the critical point: free energy; binodal line; first and second-order phase transition; critical opalescence; nucleation and growth; surface energy; critical nucleus.

• Ferromagnet-paramagnet second-order phase transition; Landau theory of phase transitions.

• Kinetic theory of gases: characteristic velocities; kinetic derivation of pressure of ideal gas; Maxwell distribution of velocities. Distribution of free paths; mean free path;

• Diffusion and random walks on a lattice model: mean-square displacement; diffusion coefficient; the diffusion equation for random walks; diffusion as transport phenomenon; derivation of Fick's laws from microscopic considerations; self- diffusion and collective diffusion coefficients.

• Other linear transport phenomena in gases: heat conductivity; Fourier law; thermalization; thermal conductivity coefficient; momentum transport; viscosity; mobility of molecules in the external field; Einstein relation; detailed balance.

• The Boltzmann equation, its derivation and stationary state. The H-theorem and its implications on the second law of thermodynamics. Derivation of the Euler equations out of the Boltzmann equation

• Advanced topics: Kubo formulas for linear transport coefficients and fluctuation-dissipation relations. From Langevin equation to Fokker-Planck equation. Thermalization in quantum systems

Bibliography