MIT Department of Physics

Building 6C-419

77 Massachusetts Avenue

Cambridge, MA 02139

USA

e-mail : jgt (at) mit.edu

Building 6C-419

77 Massachusetts Avenue

Cambridge, MA 02139

USA

e-mail : jgt (at) mit.edu

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- Jan 30, Fourth Pset due at 23:59
- Feb 2, Final exam
- Feb 4, Numerical project must have been submitted

- Notes for recitation 01: PDF, Julia code 1
- Notes for recitation 02: PDF,
- Notes for recitation 03: PDF, Julia code 1
- Notes for recitation 04: PDF,
- Notes for recitation 05: PDF,
- Notes for recitation 06: PDF, Julia code 1, Julia code 2
- Notes for recitation 07: PDF,
- Notes for recitation 08: PDF, Julia code 1, Julia code 2
- Notes for recitation 09: PDF, Julia code 1, Julia code 2
- Notes for recitation 10: PDF, Julia code 1, Julia code 2
- Notes for recitation 11: PDF, Julia code 1, Julia code 2, Julia code 3, Julia code 4
- Notes for recitation 12: PDF, Julia code 1, Julia code 2
- Notes for recitation 13: PDF

- The goal of this project is to give you an opportunity to play with some of the simulation methods exposed in the recitations. The idea is thus simple: pick a system that you like/in which you are interested, simulate it, and measure something that you find interesting. Produce the corresponding figures and write a very short report that should present the problem and the results. Submit also the Julia/Python code that you will have produced to carry out the project. This does
**not**need to be very ambitious and is really just to make sure that you can implement these methods and understand them. You should feel free to do ambitious things if you want, but this is NOT what we require (and that's not at all required to get the maximum grade). - Please validate your choice with Sunghan Ro before January 26. If you do not find your own idea for the project, please let us know before Wednesday 24 and we will come up with suggestions.
- Grading policy: you will get 20 points for completing the agreed project, 5 for the clarity of the note and 5 for having produced a clean and well-commented code.

**Prerequites:** Statistical Physics I (8.044), and Quantum Physics II (8.05).

**Lectures and Recitations: ***MTWTF 2:00-5:00
*

This course is an introduction to modern non-equilibrium statistical mechanics. We will discuss how stochastic dynamics, in and out of equilibrium, can be used to describe single or many-body systems. The methods and topics covered in the course include: Langevin and Fokker-Planck equations, master equations, ratchet currents, stochastic thermodynamics, emergent behaviors. We will study systems ranging from soft-matter physics to biophysics including colloid dynamics, bacterial motion, as well as active-matter systems. Applications outside physics will also be discussed (epidemic spreading, econophysics, sociophysics). The recitations will also include discussions of simulation methods to study non-equilibrium dynamics.

The following are useful reference books:

- C. Gardiner,
*Stochastic Methods: A Handbook for the Natural and Social Sciences* - N.G. Van Kampen,
*Stochastic Processes in Physics and Chemistry* - R. Zwanzig,
*Nonequilibrium Statistical Mechanics*

The homework assignments are an important part of this course, and the final average homework score will count for *40% of the final grade*. **You may consult with classmates in "study groups," as long as you write out your own answers. The usage of LLM is forbidden. **(See also the MIT Academic Integrity Handbook.)

There will be one homework posted every week. Problem sets are due **by 11:59 pm on the due date**. They will be turned in online through Canvas. No problem sets will be accepted after the solutions have been posted. Problem sets handed in after the 11:59 pm deadline but before the solutions have been posted are subject to a **50% grade penalty. **

Occasionally, there are problems marked as *graduate* in the problem sets. These are mandatory for the graduate students and will count as bonus points for undergraduate students. Bonus points are reported on other problem sets but the total grade cannot exceed 40%.

**1 in-class closed-book test** on 1/26/24.

The in-class test will count for 30% of the final grade.

Excuses are granted only for circumstances attested to by the Dean or a medical doctor. A student who has been excused may be required to take a makeup exam.

During the recitations, various numerical methods to simulate non-equilibrium systems will be introduced. Students will be asked to carry out the characterization of the dynamics of one non-equilibrium dynamics of their choice. Single-body physics will be acceptable for undergraduate students whereas graduate students will be required to study a many-body interacting system.

Final grades will be determined from:

- Homeworks: 40%
- In class test: 30%
- Numerical project: 30%