Test volume method

An alternative to the virial pressure route to calculating the pressure, there is a method which consists on evaluating the change in internal energy, $\Delta U$ produced by a small change in the volume of the system $\Delta V$. It can be shown that

$p={\frac {k_{B}TN}{V}}+{\frac {k_{B}T}{\Delta V}}\log \langle \exp(-\Delta U/k_{B}T)\rangle ,$

where $k_{B}$ is the Boltzmann constant and $T$ is the temperature.

The method is clearly inspired by the Widom test-particle method to obtain the chemical potential.

References

1. V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics 105 p. 8469