Test area method

The test area method is related to the test volume method for the calculation of the pressure (which, in turn, is related to Widom test-particle method). The surface tension of a planar interface is given by the change in internal energy $\Delta U$ caused by "squeezing" the system: modifying both the length in the direction normal to the interface and the area in the plane of the interface, in such a way that the total volume is left unchanged.

It can be shown that the surface tension, if the changes are small, is given by (Eq. 60):

$\gamma =-{\frac {k_{B}T}{\Delta {\mathcal {A}}}}\ln \langle \exp(-\Delta U/k_{B}T)\rangle _{0}.$

The expression parallels the one for the pressure in the test volume method; the advantages of this technique are also similar: avoidance of force calculation, easiness for discontinuous potential.