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
\[ \gamma = - \frac{ k_B T }{ \Delta {\mathcal A} } \ln \langle \exp(-\Delta U/k_B T)\rangle_0. \]
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.
