# 統力

## hw1

- Entropy of Ideal Gas, p10: http://micro.stanford.edu/~caiwei/me334/Chap7_Entropy_v04.pdf
- Heat capacity of ideal gas in term of entropy:https://en.wikipedia.org/wiki/Relations_between_heat_capacities
- Entropy elasticity: https://ethz.ch/content/dam/ethz/special-interest/mavt/process-engineering/macro-dam/documents/NetworkGels_Lecture3.pdf
- Sackur-Tetrode equation:https://physicspages.com/pdf/Schroeder/Schroeder%20Problems%2002.31-33.pdf
- Legendre transformation,p15: http://micro.stanford.edu/~caiwei/me334/Chap6_Thermodynamics_v04.pdf

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## hw2

- Holmholtz free energy in canonical ensemble:
- [derivition of F by S](https://theory.physics.manchester.ac.uk/~judith/stat_therm/node71.html#3_3helm)
- F = E - TS

- [Nernst Heat theorem](https://zh.wikipedia.org/wiki/%E8%83%BD%E6%96%AF%E7%89%B9%E7%86%B1%E5%AE%9A%E5%BE%8B),[3rd law of thermodynamics](https://zh.wikipedia.org/wiki/%E7%83%AD%E5%8A%9B%E5%AD%A6%E7%AC%AC%E4%B8%89%E5%AE%9A%E5%BE%8B)

- [Laplace transform](https://zh.wikipedia.org/wiki/%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E5%8F%98%E6%8D%A2): superposition of memonts
- moment generating function in probability theory
- [absolute convergence](https://zh.wikipedia.org/wiki/%E7%BB%9D%E5%AF%B9%E6%94%B6%E6%95%9B)
- [Leibniz rule](https://en.wikipedia.org/wiki/Leibniz_integral_rule)

- identicle correction implies the interchage of energy between identical particles.

- [Thermal wave length](https://en.wikipedia.org/wiki/Thermal_de_Broglie_wavelength)

---

Ch3.
- [volume element](https://physics.stackexchange.com/questions/188742/why-is-the-elemental-volume-of-a-sphere-equal-to-4-pi-r2dr)
- [numbers of lattice points in a sphere](https://www.jstor.org/stable/2004049?seq=1#metadata_info_tab_contents)
- [pathria 1966](https://journals.aps.org/pr/pdf/10.1103/PhysRev.151.132)
- [neumann boundry condition](https://zh.wikipedia.org/wiki/%E8%AF%BA%E4%BC%8A%E6%9B%BC%E8%BE%B9%E7%95%8C%E6%9D%A1%E4%BB%B6): gradient
- [dirichlet boundry condition](https://zh.wikipedia.org/wiki/%E7%8B%84%E5%88%A9%E5%85%8B%E9%9B%B7%E8%BE%B9%E7%95%8C%E6%9D%A1%E4%BB%B6): value
- [calculus of variation](http://file.100xuexi.com/XXSub/MatUpPT/File/201111191305521976760.pdf)
- [lagrange multiplier](https://math.stackexchange.com/questions/529416/calculus-of-variations-lagrange-multipliers)
- [calculus of variation, note](https://www.maths.ed.ac.uk/~jmf/Teaching/Lectures/CoV.pdf)
- [generating function](https://zh.wikipedia.org/wiki/%E6%AF%8D%E5%87%BD%E6%95%B0)
- [residue](https://zh.wikipedia.org/wiki/%E7%95%99%E6%95%B0)
- [Cauchy integral](https://zh.wikipedia.org/wiki/%E6%9F%AF%E8%A5%BF%E7%A9%8D%E5%88%86%E5%85%AC%E5%BC%8F)

- Question
- p52 eqn.3.2.39,
- p54 eqn.3.3.10,
- p61 eqn.3.6.5-6(S=klng)

- [nonequilibrium QFT](http://psroc.phys.ntu.edu.tw/bimonth/v25/838.pdf)

- Canonical ensemble->Boltzman distribution--p=mv-->[Maxwell distribution](https://zh.wikipedia.org/wiki/%E9%BA%A6%E5%85%8B%E6%96%AF%E9%9F%A6-%E7%8E%BB%E5%B0%94%E5%85%B9%E6%9B%BC%E5%88%86%E5%B8%83)

- the nonequilibrium correction of boltzman distribution?

- [equipartition theorem](https://zh.wikipedia.org/wiki/%E8%83%BD%E9%87%8F%E5%9D%87%E5%88%86%E5%AE%9A%E7%90%86)
- [恆星物理學](https://zh.wikipedia.org/wiki/%E8%83%BD%E9%87%8F%E5%9D%87%E5%88%86%E5%AE%9A%E7%90%86#%E6%81%86%E6%98%9F%E7%89%A9%E7%90%86%E5%AD%B8)

- harmonic oscillator
- three way of calculation:
- classical
- planck oscillator nhw
- schrodinger oscillator (n+1/2)hw

- Plank correction term (從古典出發所需要做的修正以便跟量子出發的計算結果相符)
- 一個狀態的體積(quantized state)

- 判斷相變之前要先排除2 level system的可能
- [Schottky specific heat/Schottky anomaly](https://en.wikipedia.org/wiki/Schottky_anomaly)