# 巨热力学势

（重定向自大位能

## 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 }$化學势${\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. ^ Lee, J. Chang. 5. Thermal Physics - Entropy and Free Energies. New Jersey: World Scientific. 2002.
2. ^ 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。
3. ^ Malcolm K. Brachman. Fermi Level, Chemical Potential, and Gibbs Free Energy. The Journal of Chemical Physics: 1152–1152. doi:10.1063/1.1740312.
4. ^ Hill, Terrell L. Thermodynamics of Small Systems. Courier Dover Publications. 2002. ISBN 9780486495095.