Isothermal-isobaric ensemble
From SklogWiki
The isothermal-isobaric ensemble has the following variables:
- \(N\) is the number of particles
- \(p\) is the pressure
- \(T\) is the temperature
The classical partition function, for a one-component atomic system in 3-dimensional space, is given by
\[ Q_{NpT} = \frac{\beta p}{\Lambda^{3N} N!} \int_{0}^{\infty} d V V^{N} \exp \left[ - \beta p V \right] \int d ( R^*)^{3N} \exp \left[ - \beta U \left(V,(R^*)^{3N} \right) \right] \]
where
- \( \left. V \right. \) is the Volume:
- \( \beta := \frac{1}{k_B T} \), where \(k_B\) is the Boltzmann constant
- \( \left. \Lambda \right. \) is the de Broglie thermal wavelength
- \( \left( R^* \right)^{3N} \) represent the reduced position coordinates of the particles; i.e. \( \int d ( R^*)^{3N} = 1 \)
- \( \left. U \right. \) is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)
