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Recovering the chemical potential from the correlation functions. (arXiv:2312.13144v1 [math-ph])

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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.

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