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.
[target] Students will become comfortable to use basic statistical mechanics as a useful standard tool for the earth and planetary sciences.
thermodynamics, gas molecular dynamics, micro-canonical, canonical,grand canonical ensemble, entropy, free energy, partition function
Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
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 | |
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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 |
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.
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"statistical mechanics", Landau and Lifshitz
by Homeworks, Exam, Exercise, Mini-exam
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