Course mediaThe lectures and workshops will be in person, without Zoom, and will not be recorded.
All instruction will be carried in English.
All instruction will be carried in English.
- Telegram discussion group URL
- Project Selection Choice
Thermodynamics and Statistical Mechanics 2, 2022B
About course - General
Topic outline
Lecture materials
Week 1 - Thermodynamic potentials, the extremum principle and maximum work
Week 2 - Phenomenology of phase transitions and basic terminology
Week 3 - Mean-field theory of the liquid-gas transition
Week 4 - Magnetic phase-transitions
Week 5 - Critical phenomena and continuous phase transitions
Week 6 - Spatial correlations and correlation length
Week 7 - Kinetic theory and transport
Week 8 - Transport coefficients and self-diffusion
Week 9 - Introduction to stochastic processes
Week 10 - Continuous Markov processes
Week 11 - Stochastic differential equations
Week 12 - Thermalization and the Boltzmann equation
Workshops
Week 1 - Properties of thermodynamic potentials
Week 2 - Phase coexistence
Week 3 - Lattice gas in 1D
Week 4 - Binodal, spinodal and saturation pressure of the VdW fluid
Week 5 - Mean-field of the Heisenberg model
Week 6 - Heisenberg model critical exponents and scaling hypothesis
- Week 7 - Maxwell distribution and linear transport
- Week 8 - Diffusion
- Week 9 - Markov chains
- Week 10 - Master equation
- Week 11 - Stochastic diff. eq. (Langevin's approach)
- Week 12 - Boltzmann equation
Contact information
Name Role email Building/Room Dr. Yevgeny Bar Lev Lecturer ybarlev@bgu.ac.il 54/329 Mr. Tomer Dollberg TA tomerdol@post.bgu.ac.il 54/219 Mr. Liron Tadjiev Student representative lirontad@post.bgu.ac.il
Topics and textbooks
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, 17-18Stanley, ch 2.42 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 background3 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 294-2954 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 3,4Reichl, page 1866-7 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 1.28-9 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 211 Liouville's theorem. Thermalization, ergodicity mixing and single-particle distribution function
Boltzmann equation and the H-theoremTong, ch 2
Dorfman
Huang ch 3There 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
Course policy
- 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 final exam.
Grading
Lectures (25% of final grade)
You will have to read the lecture notes before each lecture. Your primary understanding will be tested in short quizzes in Moodle at the first 5 min of every lecture.
Missed quizzes will get a grade of 0. The lowest grade will be removed.Workshops (25% of final grade)
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 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 or provide a solution after the workshop.
- 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.
- After each workshop, one of the teammates has to upload the notes of the team's work performed during the workshop.
- At least ten good effort summaries should be uploaded until the end of the course. 2 points from the final grade will be subtracted for each missing summary or summary, which the TA will determine as insufficient.
- 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.
Project (50% of final grade)
23.06.2022, from 11:00 to 15:00 (location, 27/201)
30.06.2022, from 11:00 to 15:00 (location, 54/207)Participation is mandatory.
During the project, your 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.
- 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 yourself. 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.
General
- All questions relevant to more than one person should be asked via the Questions and answers forum, the Telegram group, 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.