Course: Thermodynamics and Statistical Mechanics 2 - 2023B

  • 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
    5Critical 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
    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.

    • Callen - Thermodynamics
    • Dorfman and Beijeren - The Kinetic Theory of Gases (1977)
    • Fermi - Thermodynamics
    • Huang - Statistical Mechanics
    • Gardiner - Handbook of stochastic methods (4th edition)
    • Goldenfeld - Lectures On Phase Transitions And The Renormalization Group
    • Kittel and Kroemer - Thermal Physics
    • Reichl - A Modern Course in Statistical Physics
    • Reif - Fundamentals of Statistical and Thermal Physics
    • Stanley - Introduction to Phase Transitions and Critical Phenomena
    • Tong - Lecture notes on kinetic theory
    Chemisty background

  • Grading

    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)


    • During the semester, you will be divided into teams of 4-6 teammates. All of the team activities will be done with the same team.
    • You will be evaluated according to your team's performance and your performance throughout the semester.

    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.

    • Your teammates will give your grade for the workshops in 2 anonymous peer evaluation sessions during the semester. The first peer evaluation will be for practice only and will not be counted towards your grade, but participation in both  peer evaluations is mandatory to get the workshop grade. Note that the peer evaluation grade will be normalized.
    • Using existing solutions of the workshop exercises before or during the workshop session is entirely pointless, and it is detrimental to your learning and your team's learning.
    • As such, we will consider this as a professional ethics violation.
    Home Exercises
    Following the workshops, additional problem sets will be published for self-practice. While they will not be graded or collected by staff, we highly encourage you to work through them to the best of your ability and seek assistance from the staff if needed. As mentioned, the quizzes will be partly based on these problems.


    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:

    • Assessment by external experts. If possible, your deliverable will be evaluated by an external committee of faculty members. Otherwise, the course staff will serve as such a committee. The deliverable will be evaluated on scientific content and originality and effectiveness of passing the knowledge to others (60% of project grade).
    • The team assesses the individual contribution of each of its teammates to the project (20% of project grade).
    • Assessment by other teams (20% of project grade)
    • Assessment precision (each team will be awarded +0.5 points to their project grade if their evaluation of another team is within 7 points of the average evaluation of the experts. If it differs by more than 12 points, 1 point will be subtracted)
    Professional ethics (up to -10 points of final grade)

    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.

    • Decide on team rules/code. Set expectations.
    • Respectful and calm conversation
    • Avoid performing unilateral decisions
    • Keep communication channels open
    • Do not take over the team
    • Give equal opportunities to everyone
    • Avoid sensitive or provocative topics
    • Be considerate of your teammates' needs
    • Avoid unethical behavior, which can poorly reflect on your teammates

    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.

    • All questions relevant to more than one person should be asked via the Questions and answers forum, Perusall or the class representatives.
    • Personal questions should be addressed to the TA.
    • If you cannot attend the lectures/workshops due to a formally accepted reason, please contact the TA. Such workshops and lectures will not be counted towards your grade. 
    • If you miss any team activity, for whatever reason, be a good team player and inform your team in advance. Not doing so might harm your peer evaluation.