# 大位能

## 定义

${\displaystyle J\;{\stackrel {\mathrm {def} }{=}}\ U-TS-\mu N}$

${\displaystyle U}$ 内能${\displaystyle T}$ 是系統的溫度${\displaystyle S}$ ${\displaystyle \mu }$ 化學位能${\displaystyle N}$ 是系統中的粒子數。

${\displaystyle dJ=-SdT-Nd\mu -pdV}$

### 朗道自由能

${\displaystyle \Omega \ {\stackrel {\mathrm {def} }{=}}\ F-\mu N=U-TS-\mu N}$

## 均相系的巨热力学势

${\displaystyle \left({\frac {\partial \langle p\rangle }{\partial V}}\right)_{\mu ,T}=0}$

${\displaystyle \left({\frac {\partial \langle N\rangle }{\partial V}}\right)_{\mu ,T}={\frac {N}{V}}}$

${\displaystyle J=-\langle p\rangle V}$

${\displaystyle G=\langle N\rangle \mu }$

## 理想气体的巨热力学势

${\displaystyle J=-k_{\mathrm {B} }T\ln \Xi =-k_{\mathrm {B} }TZ_{1}\mathrm {e} ^{\beta \mu }}$

## 參考

1. ^ Agata Fronczak. Microscopic meaning of grand potential resulting from combinatorial approach to a general system of particles (PDF). [2019-07-29]. （原始内容 (PDF)存档于2019-07-29）.
2. ^ Lee, J. Chang. 5. Thermal Physics - Entropy and Free Energies. New Jersey: World Scientific. 2002.
3. ^ David Goodstein. States of Matter, pp.19. 提到朗道势能（Landau potential）是${\displaystyle \Omega =F-\mu N\,\;}$  ，這裡的F是亥姆霍茲自由能。
4. ^ Malcolm K. Brachman. Fermi Level, Chemical Potential, and Gibbs Free Energy. The Journal of Chemical Physics: 1152–1152. [2018-04-02]. doi:10.1063/1.1740312. （原始内容存档于2021-05-07）.
5. ^ Hill, Terrell L. Thermodynamics of Small Systems. Courier Dover Publications. 2002. ISBN 9780486495095.