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 | |
---|---|---|
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 | Summary | total summary |
Class 15 | Essence of statistical mechanics | statistical mechanics minimum, what is not yet understood |
none
"statistical mechanics", Landau and Lifshitz
by Homeworks, Exam, Exercise, Mini-exam
none