Ruprecht Karls Universität Heidelberg

Statistical Physics (MKTP1) Winter Term 2012/13


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 many-particle-systems therefore has to be a statistical one. This lecture provides an introduction to the fundamentals and main applications of statistical physics for first-year 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 non-equilibrium statistical physics or complex systems. Some examples of on-going research will be included in this course.

Being part of the master studies, the lectures will be given in English. There are two lectures each week, from 11.15-12.45 (no break) in the large lecture hall at Philosophenweg 12. The exercises will be organized by Thorsten Erdmann and registration occurs as usual through the webpages of the Institute for Theoretical Physics. Exercises will be handed out during the exercises on Friday and have to be returned one week later. Students are allowed to work together in groups of up to three. 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 will be written in parallel with the lectures by Stephan Eismann and Ulrich Schwarz.

The exam has been scheduled for Friday February 8 2013 from 9.30 -12.30 am in the two lecture halls HS1 and HS2 in INF 308. Participants are allowed to bring one DinA4-sheet with notes (on both sides). Please also bring an ID-card. Calculators are neither allowed nor necessary. You need to achieve at least 30 percent of correct solutions to pass the exam.

Those who have not reached the 30 percent or have been ill can take the second exam (Nachklausur). It will take place in the large lecture room at Philosophenweg 12, on Thursday April 4 from 10 am - 1 pm.


  1. Probability theory: random variables, probability distributions, moments, central limit theorem, random walks, information entropy (Shannon), mutual information, principle of maximal entropy (Jaynes)
  2. Equilibrium ensembles: microcanonical, canonical and grandcanonical ensembles, ideal gas, thermodynamic potentials, Legendre transformations, Maxwell relations, material properties, thermodynamic engines, work and heat, laws of thermodynamics
  3. Ideal quantum systems: Fermi gas, Bose gas, photons, Stefan-Boltzmann law, Planck radiation formula, Bose-Einstein condensation, phonons, specific heat of solids, Einstein model, Debye model
  4. Classical fluids: real gases, virial expansion, van der Waals-fluid, Maxwell-construction, phase diagrams, critical phenomena
  5. Magnetic systems: lattice gases, 1D and 2D Ising model, Peierls argument for phase transition, Onsager solution, Landau theory, field theory, path integrals, renormalization group
  6. Numerical methods: ergodic theorem, molecular dynamics, thermostat, importance sampling, Monte Carlo methods, Metropolis algorithm, data analysis, regression, boot strapping
  7. Dynamics and non-equilibrium physics: Brownian motion, master equation, Fokker-Planck equation, Langevin equation, fluctuation-dissipation theorem, stochastic thermodynamics, fluctuation theorems

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 up-do-date 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

Classical textbooks

  • Landau-Lifshitz volume 5
  • Frederick Reif, Fundamentals of Statistical and Thermal Physics, Macgraw-Hill 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

Book with applications to soft matter and biological physics

  • Ken Dill and Sarina Bromberg, Molecular Driving Forces: Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience, revised edition, Garland 2010

Scripts by local lecturers

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