2024 Faculty Courses School of Science Undergraduate major in Earth and Planetary Sciences
Statistical Mechanics (EPS course)
- Academic unit or major
- Undergraduate major in Earth and Planetary Sciences
- Instructor(s)
- Bunei Sato / Taishi Nakamoto
- Class Format
- Lecture/Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-8 Mon / 5-8 Thu
- Class
- -
- Course Code
- EPS.B332
- Number of credits
- 220
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course is primarily for beginners who need a basic understanding of statistical mechanics starting from a summary of thermodynamics.
The classical gas molecular theory helps to grasp the basic concept of probability distribution to micro-canonical, canonical, and grand canonical ensembles. Some applications are shown.
Course description and aims
[Target] Students will become comfortable to use basic statistical mechanics as a useful standard tool for the Earth and planetary sciences.
Keywords
thermodynamics, gas molecular dynamics, micro-canonical, canonical,grand canonical ensemble, entropy, free energy, partition function
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Starting with a brief summary of the previous lecture I will give a simple homework assignment to
help students gain a better understanding. At the end of the course an overall summary is given.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Thermodynamics（１） | Basic concepts of thermodynamics, Helmholtz's free energy |
| Class 2 | Thermodynamics（２） | Internal energy, Heat, Entropy |
| Class 3 | Gas molecular theory (1) | Gas pressure, Maxwell's distribution |
| Class 4 | Gas molecular theory (2) | Applications: Averages, Collision Number, Mean Free Path, Absorption Line Width |
| Class 5 | Micro-canonical statistics (1) | Principle of equal a priori probabilities |
| Class 6 | Micro-canonical statistics (2) | Boltzmann’s formula |
| Class 7 | Micro-canonical statistics (3) | Applications: Rubber, Ideal Gas, Harmonic Oscillator |
| Class 8 | Canonical statistics（（３） | Derivation from micro-canonical statistics, Helmholtz’ free energy |
| Class 9 | Canonical statistics（２） | Partition function、Boltzmann factor |
| Class 10 | Grand canonical statistics | Gibbs’ free energy、Chemical potential |
| Class 11 | Quantum statistical mechanics（１） | Bose statistics、Bose-Einstein condensation |
| Class 12 | Quantum statistical mechanics（２） | Fermi statistics、Fermi degeneracy |
| Class 13 | Application of statistical mechanics to astrophysics | White dwarf、Neutron star、Chandrasekhar limit |
| Class 14 | Comprehension check | Comprehension check |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
none
Reference books, course materials, etc.
"statistical mechanics", Landau and Lifshitz
Evaluation methods and criteria
Homeworks, Exercise, Mini-exam (50%), and Comprehension check (50%)
Related courses
- EPS.B202 ： Thermodynamics (EPS course)
- EPS.B331 ： Quantum Mechanics (EPS course)
Prerequisites
none
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
satobn[at]eps.sci.titech.ac.jp
nakamoto[at]eps.sci.titech.ac.jp