Virial pressure

The virial pressure is commonly used to obtain the pressure from a general simulation. It is particularly well suited to molecular dynamics, since forces are evaluated and readily available. For central interactions, one has:

$p=\frac{k_{B}TN}{V}-\frac{1}{dV}\overline{{\sum }_{i<j}{\mathbf{f}}_{ij}{\mathbf{r}}_{ij}},$

where one can recognize an ideal term, and a second term due to the virial. The overline is an average, which would be a time average in molecular dynamics, or an ensemble average in Monte Carlo; $d$ is the dimension of the system (3 in the "real" world). ${\mathbf{f}}_{ij}$ is the force on particle $i$ exerted by particle $j$, and ${\mathbf{r}}_{ij}$ is the vector going from $i$ to $j$: ${\mathbf{r}}_{ij}={\mathbf{r}}_j-{\mathbf{r}}_i$.