  Interacting particle systems in a finite-volume in equilibrium are often
described by a grand-canonical ensemble induced by the corresponding
Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly
measuring this Hamiltonian is not possible, as such, methods need to be
developed to calculate the Hamiltonian potentials from measurable data. In this
work, we give an expansion of the chemical potential in terms of the
correlation functions of such a system in the thermodynamic limit. This is a
justification of a formal approach of Nettleton and Green from the 50's, that
can be seen as an inverse cluster expansion.
