Instructions: Clicking on the section name will show / hide the section.
| Week | Topic | Additional reading |
|---|---|---|
| 1 | Thermodynamic potentials, the extremum principle and maximum work. Convex properties of thermodynamic potentials, thermodynamic stability, response functions. Legendre transform and its geometric meaning. | Callen, ch 3.1, 3.3 Fermi, ch IV, 11-13, ch V, 17-18 Stanley, ch 2.4 |
| 2 | Types of phase-transitions: thermal, quantum, dynamical. Long-range order. Spontaneous symmetry breaking. Role of thermodynamic limit. Role of quantum mechanics. Ehrenfest and modern classification of thermal phase-transitions. Importance of interactions for phase-transitions. Origin of intermolecular forces (IMF). Phenomenology of first order phase transitions: experimental observations; thermodynamic phases, conditions for phase equilibrium. Clausius-Clapeyron equation. | Stanley, ch 1.1 Kittel, chapter 10, p 275-297 Callen ch 5, 6, 8 Kittel, ch 10 Chemistry background |
| 3 | Interacting gases, mean-field theory of the liquid-gas transition - van der Waals gas. Thermodynamics properties of the vdw equation, and its critical temperature. Equation of corresponding states, and Maxwell construction. Surface tension, supercooling and superheating, spinodal and binodal lines. |
Stanley, ch 5 Huang, ch 2 Fermi, ch IV, 16 Kittel, chapter 10, p 294-295 |
| 4 | Magnetic phase transition transition |
Stanley, chapter 6 |
| 5 | Critical phenomena, spontaneous-symmetry breaking, critical exponents and universality. Correlations and correlation length, critical opalescence. Peierls-Landau criteria. Role of quantum mechanics in thermal phase transitions. |
Stanley, chapter 3, 5.5, 6 Goldenfeld, chapter 3,4 Reichl, page 186 |
| 6-7 | Introduction to nonequilibrium statistical mechanics, Maxwell distribution, mean-free path and relaxation time Transport coefficients: diffusion, thermal conductivity and viscosity. From conservation laws to diffusion equation. |
Kittel ch 14 Reichl ch 9.2 Reif ch 12 Tong, Section 1.2 |
| 8-9 | Markov processes: Markov chains, continuous-time stochastic processes and the master equation. Stationary state and detailed balance. |
Gardiner, ch 3 |
| 10 | Continuous Markov processes, Langevin equation and fluctuation-dissipation relation | Dorfman Tong, ch 2 |
| 11 | Liouville's theorem. Thermalization, ergodicity mixing and single-particle distribution function Boltzmann equation and the H-theorem |
Tong, ch 2 Dorfman Huang ch 3 |
There is no one main textbook in the course. Some of the books, which are relevant to the course are listed bellow. The relevant chapters could be read from the table above.
Two quizzes: 40% of final grade, based on the workshops and self-practice questions, as also conceptual questions asked during the lectures.
Quiz 1: 19.05.2023 at 09:00-12:00
Quiz 2: 16.06.2023 at 09:00-12:00
Workshops (peer assessment): 10%
Project presentation (panel and peer assessment: 50%
Presentation 1: 26.06.2023 at 14:00-18:30 (51/015)
Presentation 2 [f needed]: 26.07.2023 at 13:30-18:30 (51/015)
Teamwork
There will be no passive tutorials in this course. Namely, a session where the TA solves exercises on the "board," however, such a tutorial session will be recorded by the TA in advance and available for you to watch.
The recording will usually be less than 50 minutes long, and you must watch it before you attend a workshop
and mark it as completed in Moodle. Not doing so will make the workshop entirely pointless for you and diminish your ability to contribute to your team. During the workshop, which will take two academic hours, you will work within your teams
on problem sets distributed by the TA. The TA will provide help, as needed, but will not solve the problem sets. Solutions for most problems will be available in the same Moodle quiz after the workshop.
Before leaving the workshop you need to show to the TA the outcome of your work in the workshop. This is meant to verify that you have devoted adequate effort during the workshop and not necessarily to verify the correctness of your work.
The participation in the project presentation is mandatory both as presenters and as audience.
During the project, you will deepen and extend your knowledge beyond the course syllabus. Each team will choose and learn an advanced topic and later explain it to other teams in a short presentation of about 30 min at the end of the semester. You can
choose how to present the material to your classmates: lecture, presentation, movie, game, or experiment. Anything goes, as long as you can pass what you learned to your classmates. So be creative. Also, your team can extend or provide an alternative
direction or deliverable to the project, pending permission of the staff.
The list of projects should be available around Passover, and it will include more analytically and more numerically inclined projects. The choice of the project will be on a first-come, first-serve basis, so pay attention or negotiate with other teams. If you cannot agree between yourselves, we will randomly divide the projects.
You must present to the staff (as a group) a satisfactory work-plan not later than one week after the first quiz.
This should include the precise topic, initial plan of exposition and division of roles / work between the group members.
Failure to provide a satisfactory work-plan will result in subtraction of up to 10 points from the final grade.
The
project's grade will be composed from:
Your professional lives outside the university's walls will often involve teamwork. One of the goals of the workshops is to help you be a better team player.
Note that it will involve a certain effort on your side since it is not always easy to get along with other people. You do not need to be friends with your teammates, but it is crucial to keep professional and, most importantly, respectful relationships within your team. Keeping the basic guidelines below should help you create a productive and healthy atmosphere within your team.
If conflicts arise, we expect you to solve them by yourselves. We will only intervene in extreme cases, such as trolling, bullying, shaming, or non-honest behavior that the team could not resolve. In such a case, we will invite the team for clarification. Typically, we will suggest ways to resolve the problem or issue a warning; however, some cases will result in a penalty to the offender's grade.
Course media