
Theoretical Statistical Physics Winter Term 2017/18
Introduction
Statistical physics deals with the properties of physical systems with many particles. For macroscopic systems like gases, liquids and solids, we know today that they typically contain 6x10^23 particles (Avogadro number). For systems with that many particles, it is neither possible nor desirable to follow all the details of the microscopic dynamics, irrespective of whether the system of interest is of classical or quantum nature. A reasonable description of manyparticlesystems therefore has to be a statistical one. This lecture provides an introduction to the fundamentals and main applications of statistical physics for firstyear master students. It can also be attended by interested bachelor students who have completed the four introductory courses in theoretical physics. In contrast to other fundamental fields of theoretical physics, such as mechanics or electrodynamics, there is still a lot of current research in statistical physics, for example in regard to nonequilibrium statistical physics or complex systems. Some examples of ongoing research will be included in this course. Statistical physics is everywhere and examples for application areas are condensed matter physics, astrophysics and biophysics.
Being part of the master studies, the lectures will be given in English. There are two lectures each week, on Tuesday and Thursday from 11.1512.45 (no break) in the large lecture hall at Philosophenweg 12. The exercises will be organized by Falko Ziebert and registration occurs as usual through the webpages of the department of physics and astronomy. Each week there is a new sheet of exercises provided through the web and solutions have to be handed in one week later. Students are allowed to work together in groups of up to two. In order to be allowed to the final exam, you have to solve successfully more than half of the exercises. Some exercises will involve computer programming on an elementary level. A script is available from an earlier version of this course (winter term 2015/16) and will be improved during this one.
Content
 Probability theory: random variables, probability distributions, moments, central limit theorem, random walks, information entropy (Shannon), mutual information, principle of maximal entropy (Jaynes), conditional probabilities, Bayes' theorem
 Equilibrium ensembles: microcanonical, canonical and grandcanonical ensembles, ideal gas, thermodynamic potentials, Legendre transformations, Maxwell relations, material properties, thermodynamic engines, work and heat, chemical reactions
 Ideal quantum systems: Fermi gas, Bose gas, photons, StefanBoltzmann law, Planck radiation formula, BoseEinstein condensation, phonons, specific heat of solids, Einstein model, Debye model
 Classical fluids: real gases, virial expansion, van der Waalsfluid, Maxwellconstruction, phase diagrams, critical phenomena
 Magnetic systems: lattice gases, 1D and 2D Ising model, Peierls argument for phase transition, Onsager solution
 Numerical methods: molecular dynamics, thermostat, importance sampling, Monte Carlo methods, Metropolis algorithm
 Dynamics and nonequilibrium physics: Brownian motion, random walks, FokkerPlanck equation, Langevin equation, fluctuationdissipation theorem
Material for the course
Recommended literature
The usual suspects
 Thorsten Fliessbach, Statistische Physik, Lehrbuch zur Theoret. Physik IV, Spektrum
 Wolfgang Nolting, Grundkurs Theoretische Physik 6, Statistische Physik, Springer
Other updodate textbooks
 Franz Schwabl, Statistische Mechanik, 3. Auflage, Springer 2006
 Josef Honerkamp, Statistical Physics, 2nd edition, Springer 2002
 Luca Peliti, Statistical Mechanics in a Nutshell, Princeton University Press 2011
 James Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity, Oxford Master Series in Physics 2006
Classical textbooks
 LandauLifshitz volume 5
 Frederick Reif, Fundamentals of Statistical and Thermal Physics, MacgrawHill 1965
 Herbert Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edition, John Wiley & Sons 1985
 Kerson Huang, Statstical Mechanics, 2nd edition, John Wiley & Sons 1987
 Terrell L. Hill, An Introduction to Statistical Thermodynamics, Dover 1960
 Donald McQuarrie, Statistical mechanics, Univ Science Books 2000
 David Chandler, Introduction to Modern Statistical Mechanics, Oxford Univ Pr 1987