Statistical Physics B

The students entering the course are expected to have completed an introductory course on statistical physics and thermodynamics as well as the standard undergraduate level courses (classical and quantum mechanics, electrodynamics). Some knowledge of fluid mechanics and stochastic processes is useful.

Statistical physics is the branch of physics that describes many-body systems with methods from probability theory and statistics. Fundamentally, it describes a link between the microscopic world governed by, for example, classical or quantum mechanics, and the macroscopic world governed by thermodynamics. Later it was found that general methods of statistical physics can be even applied to other systems, such as financial markets or social networks.

Typically, introductory courses in statistical physics discuss ensemble theory with several applications to ideal systems in equilibrium. In Statistical Physics B, we go a step further by discussing interacting systems and out-of-equilibrium systems.

1. Recap of ensemble theory and ideal systems

2. Statistical mechanics of classical interacting systems: Mayer expansion, pair correlation function, structure factor, Ornstein-Zernike relation, closure relations, hard-sphere fluids.

3. Systems in an external potential, inhomogeneous systems, density functional theory.

4. Phase behaviour, phase diagrams, spinodal, binodal.

5. Effective interactions

6. Foundations of linear irreversible thermodynamics, minimum entropy production principle, Onsager reciprocity, Curie principle.

7. Brownian motion, fluctuation-dissipation theorem, linear response theory, self-diffusion and collective diffusion.

8. Elements of kinetic theory, H theorem, hydrodynamic limit.

R. K. Pathria and P. D. Beale, Statistical Mechanics

K. Huang, Statistical mechanics

F. Schwabl, Statistical mechanics

R.H. Swendsen, An introduction to statistical mechanics and thermodynamics

F. Mandl, Statistical physics

H.B. Callen, Thermodynamics

J. K. G. Dhont – An introduction to the dynamics of colloids

S. R. de Groot and P. Mazur – Non-equilibrium thermodynamics

J.-P. Hansen and I. R. MacDonald - Theory of simple liquids

J.R. Dorfman, H. van Beijeren, and T. R. Kirkpatrick, Contemporary kinetic theory of matter

The student will have a working knowledge of how to apply statistical mechanics in and out of equilibrium.

Mid-term exam (30%), hand-in exercises (30%), final exam (40%).