### 2020　Statistical Mechanics (EPS course)

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Undergraduate major in Earth and Planetary Sciences
Instructor(s)
Sato Bunei  Hosoya Akio
Course component(s)
Lecture / Exercise    (ZOOM)
Day/Period(Room No.)
Tue5-8(W932)  Fri5-8(W932)
Group
-
Course number
EPS.B332
Credits
4
2020
Offered quarter
4Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

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.

### Student learning outcomes

[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 that will be developed

 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/Required learning

Course schedule Required learning
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、 　Boltzmann’s formula、ideal gas
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 Examination Examination

### Out-of-Class Study Time (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.

none

### Reference books, course materials, etc.

"statistical mechanics", Landau and Lifshitz

### Assessment criteria and methods

by Homeworks, Exam, Exercise, Mini-exam

### Related courses

• EPS.B202 ： Thermodynamics (EPS course)
• EPS.B331 ： Quantum Mechanics (EPS course)

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