Isothermal-isobaric ensemble

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

$Q_{NpT}={\frac {\beta p}{\Lambda ^{3N}N!}}\int _{0}^{\infty }dVV^{N}\exp \left[-\beta pV\right]\int d(R^{*})^{3N}\exp \left[-\beta U\left(V,(R^{*})^{3N}\right)\right]$

where

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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. $\int d(R^{*})^{3N}=1$

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. U \right. } is the potential energy, which is a function of the coordinates (or of the volume and the reduced coordinates)

References

1. D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press