Widom test-particle method

The excess chemical potential is given by

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where $k_{B}$ is the Boltzmann constant, T is the temperature, N is the number of particles within the system and $\Phi$ is the intermolecular pair potential.

References

1. B. Widom "Some Topics in the Theory of Fluids", Journal of Chemical Physics 39 pp. 2808-2812 (1963)
2. B. Widom "Potential-distribution theory and the statistical mechanics of fluids", Journal of Physical Chemistry 86 pp. 869 - 872 (1982)
3. David S. Corti "Alternative derivation of Widom's test particle insertion method using the small system grand canonical ensemble", Molecular Physics 93 pp. 417-420 (1998)