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Covers the study of (primarily homogeneous) macroscopic systems from a heat/energy/entropy point of view. Consider also using the tag: [statistical-mechanics].

1 vote

Thermodynamic free energy

The weight for a specific state is $w(\phi)=e^{-E/T+F/T}\equiv e^{-I(\phi)+F/T}$. Due to the definition of the entropy $S$, we have $S=-\int D\phi w\ln w=\frac{1}{T}(\int D\phi wE-F\int D\phi w)=\frac …
Wen Chern's user avatar
  • 271
2 votes

The average value of the electric polarization of an ideal gas

It is better to work with the spherical coordinate system. Then the integral takes the form: $\int drd\theta d\phi r^2\sin\theta e^{\frac{1}{kT}ED\cos\theta}\\ =\int drd\cos\theta d\phi r^2 e^{\frac{1 …
Wen Chern's user avatar
  • 271
1 vote
Accepted

Chemical Potential in the canonical and grand canonical ensemble

In statistical mechanics, we always consider systems at thermodynamic limit. By thermodynamic limit, we mean that the volume or the number of particles of a system tends to infinity. It can be shown t …
Wen Chern's user avatar
  • 271