2021 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 / Akio Hosoya
- Class Format
- Lecture/Exercise
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-8 Mon (H112) / 5-8 Thu (H112)
- Class
- -
- Course Code
- EPS.B332
- Number of credits
- 220
- Course offered
- 2021
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 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, which may be helpful for the exam.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Thermodynamics（１） |
The first law, what is heat? |
| Class 2 | Thermodynamics（２） |
Carnot’s principle, entropy |
| Class 3 | gas molecular theory |
Maxwell's distribution, Bernoulli’s relation |
| Class 4 | Thermodynamics and statistical mechanics |
macroscopic and microscopic physics |
| Class 5 | Micro-canonical statistics |
principle of equal a priori probabilities、 |
| Class 6 | Canonical statistics（１） |
Derivation from microcanonical statistics、Helmholtz’ free energy |
| Class 7 | Canonical statistics（２） |
Partition function、Boltzmann factor |
| Class 8 | Canonical statistics（（３） |
Free particles, Harmonic ocsillator |
| Class 9 | Grand canonical statistics |
Gibbs’ free energy、Chemical potential |
| Class 10 | Quantum statistical mechanics（１） |
Bose statistics、Bose-Einstein condensation |
| Class 11 | Quantum statistical mechanics（２） |
Fermi statistics、Fermi degeneracy |
| Class 12 | Application of statistical mechanics to astrophysics（１） |
White dwarf、Neutron star、Chandrasekhar limit |
| Class 13 | Application of statistical mechanics to astrophysics（２） |
Nucleosynthesis |
| Class 14 | Summary |
Pick up important points |
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
by Homeworks,the final Report, Exercise, Mini-exam
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).
ahosoya.bongo[at]gmail.com