Test area method

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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 [1] (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.