Welcome to the course of Statistical Mechanics and Thermodynamics. The course will follow the schedule below, where you can also find the link to the weekly exercises. Most of the exercises are taken from a set of about 200 problems that cover most of the material (the full file here).
The final exam will also be based on these set of problems.
Example of the 2018 Spring Semester exam can be found here: Exam-2018
The course will be taught by Jairo Sinova and Karin Everschor-Sitte jointly. Office hours should be arranged according to need.
The class and exercise schedule is as follows:
Theoretische Physik 4, Statistische Physik Sinova, Everschor-Sitte
Montag 8:00 - 10:00, Lorentz-Raum
Dienstag 12:00 - 14:00, Lorentz-Raum
Übungen zur Theoretischen Physik 4 Sinova, Everschor-Sitte mit Ass.
Dienstag 14:00 - 16:00, Seminarraum A
Mittwoch 10:00 - 12:00, Seminarraum A
Donnerstag 14:00 - 16:00, Seminarraum C
The literature that we will follow is
[1] R. K. Pathrida and Paul D. Beale, Statistical Mechanics, Third Edition.
[2] K. Huang, Statistical Mechanics (Wiley, New York, 1987)
| 1 | Mo, 15. Oct. 2018 08:00 |
Introduction Concepts and definitions in thermodynamics: thermodynamic variables, state functions, quasi-static processes, etc. Reversible and irreversible processes and examples. Exercise Assignment 1 (Due 29th Oct) |
[2] 1.1 |
| 2 | Di, 16. Oct. 2018 12:00 |
1st Law of Thermodynamics: General principles of thermodynamic and its laws. Introduction of the different thermodynamic potentials. |
[2] 1.2-1.7 |
| 3 | Mo, 22. Oct. 2018 08:00 |
2nd Law of Thermodynamics: Maxwell relations and Examples Exercise Assignment 2 (Due 5th Nov) |
[2] 1.6 |
| 4 | Di, 23. Oct. 2018 12:00 |
Thermodynamic potentials as generation functions: calculation of different thermodynamic variables (P,V from the 1st derivatives, heat capacity as a 2nd derivative). |
2] 1.1-1.7 |
| 5 |
Mo, 29. Oct. 2018 08:00 |
3rd Law of Thermodynamics | [2] 1.1-1.7 |
| 6 | Di, 30. Oct. 2018 12:00 |
Thermodynamics review and examples Hands on exercise on melting ice (YouTube) |
2] 1.1-1.7 |
| 7 | Mo, 5. Nov 2018 8:00 |
Statistical view of Entropy Ideal gas from a statistical perspective |
[1] 1.1-1.4, 2.1-2.4[2] 6.1, 6.2 |
| 8 |
Di, 6. Nov. 2018 12:00 |
Gibbs paradox |
[1] 1.1-1.4, 2.1-2.4[2] 6.1, 6.2 |
| 9 | Mo, 12. Nov. 2018 8:00 |
Ensemble Theory Phase space and dynamics of the classical multi-body system. Probability function, Liouville's theorem, Ensemble theory, brief introduction of the different ensembles. Microcanonical ensemble |
[1] 3.1-3.5 [2] 7.1 |
| 10 | Di, 13. Nov. 2018 12:00 |
The Canonical ensemble the Gibbs’ postulate for the distribution function, the partition function, relation with the thermodynamic potentials |
[1] 3.1-3.5 [2] 7.1 |
| 11 | Mo, 19. Nov. 2018 08:00 |
Examples using the canonical ensemble: Harmonic oscillator systems (classical and quantum mechanical), paramagnetism, and negative temperature |
[1] 3.7-3.10, 16.3.A |
| 12 | Di, 20. Nov. 2018 12:00 |
The grand canonical ensemble Consistency of the postulates for the different ensembles |
[1] 4.1-4.5, 3.6 [2] 7.3, 7.6 |
| 13 | Mo, 26. Nov. 2018 08:00 |
Special lecture by Assa Auerbach: Max the Demon vs. Entropy of Doom |
|
| 14 | Di, 28. Nov. 2018 12:00 |
Quantum systems: Density matrix vs distribution function. Quantum canonical and grand canonical ensemble. | [1] 5.1-5.5 [2] 8.1, 8.2 |
| 15 |
Mo, 3. Dec. 2018 08:00 |
Examples: an electron in a magnetic field and free particles in a box | [1] 5.1-5.5 [2] 8.1, 8.2 |
| 16 | Di, 4. Dec. 2018 12:00 |
Examples: Ideal gas of the harmonic oscillator (3.8), discrete level distribution function (black body 7.3); |
[1] 3.8-3.10 (7.3) |
| 17 | Mo, 10. Dec. 2018 08:00 |
Fermi- and Bose statistics. Indiscernibility of the quantum particles. Symmetry and anti-symmetry of wave functions. Fermi and Bose statistics. Fermi-Dirac and Bose-Einstein distributions for an ideal gas: derivation using the grand canonical ensemble. | [1] 5.4,6.1,6.2,6.3 [2] A.1, A.2, 8.5,8.6 |
| 18 | Di, 11. Dec. 2018 12:00 |
(continuation) Fermi-Dirac and Bose-Einstein distributions for an ideal gas: derivation using the grand canonical ensemble.
|
[1] 5.4,6.1,6.2,6.3 [2] A.1, A.2, 8.5,8.6 |
| 19 | Mo, 17. Dec. 2018 08:00 |
Bose-gas: Equation of state of the photon gas (black body problem). Black-body catastrophe. | [1] 7.1,7.3 [2] 12.1-12.3 |
| 20 | Di, 18. Dec. 2018 12:00 |
Bose-gas: (cont) Equation of state of the phonon gas in solids (two limiting cases of low and high temperatures). Bose-Einstein condensationExercises for Assignment 8 (Due 7th Jan) |
[1] 7.1,7.4,7.2 [2] 12.1-12. |
| 21 | Mo, 7. Jan. 2019 08:00 |
Fermi-gas: Equation of state for electron gas in metals and magnetism* of ideal Fermi gas | [1] 8.1,8.3,8.2* [2] 11.1,11.3* |
| 22 | Di, 8. Jan. 2018 12:00 |
Fermi-gas: continued
|
[1] 8.1,8.3,8.2* [2] 11.1,11.3* |
| 23 | Mo, 14. Jan. 2019 08:00 |
Non-ideal gas and Interacting systems: Equation of state of the non-ideal gas (cluster expansion and Virial expansion – van der Walls) Role of correlations, hints for derivation. |
[1] 10.1-10.3,10.7 |
| 24 | Di, 15. Jan. 2018 12:00 |
Fluctuation theory Fluctuations and concept of local equilibrium. Exercises for Assignment 9 (Due 21st Jan) |
[1] 15.1 |
| 25 | Mo, 21. Jan. 2019 08:00 |
Thermodynamics of Phase Transitions Definition of phases and phase transition. Phase Equilibrium and the Clausius-Clapeyron relation. Classification of the phase transitions (Ehrenfest). |
[1] 4.6, 4.7 [2] 2.1, 2.2 |
| 26 | Di, 22. Jan. 2018 12:00 |
Phase transitions: criticality, universality, and scaling Liquid-gas (based on van-der-Waals equation). Exercises for Assignment 10 (Due 28th Jan) |
[1] 12.1, 12.2 [2] 17.5, 17.6 |
| 27 | Mo, 28. Jan. 2019 08:00 |
Landau theory of phase transitions. | [1] 12.7, 12.9,12.10 [2] 13.4, 17.1-17.3 |
| 28 | Di, 29. Jan. 2018 12:00 |
Scaling Theory: The scaling approach to phase transitions (Kadanoff hypothesis, etc.)Exercises for Assignment 11 (Due 4th Feb) |
[1] 12.10, 12.11, 12.12 |
| 29 | Mo, 4. Feb. 2019 08:00 |
Phase Transitions: some exact models | [1] 13.2 |
| 30 | Di, 5. Feb. 2018 12:00 |
Introduction to Renormalization Group Theory of Phase Transitions | [1] 14.1-14.3 |
| 31 | Mo, 11. Feb. 2019 08:00 |
Course Review | |
| 32 | Di, 12. Feb. 2018 12:00 |
FINAL EXAM |
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