Prerequites: Statistical Physics I (8.044), and Quantum Physics II (8.05).
Lectures and Recitations: MTWTF 2:00-5:00
Grade: 4 Problem sets, 1 numerical project, 1 final exam. See below for detail.
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:
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: