An inversion formula for the 2-body interaction given the correlation functions

TL;DR

This paper proves the convergence of an expansion for the pair interaction potential of a classical gas using all-order truncated correlation functions at infinite volume.

Contribution

It introduces an inversion formula that reconstructs the interaction potential from correlation functions, demonstrating convergence in the infinite-volume limit.

Findings

Established an explicit expansion for the pair potential.

Proved convergence of the expansion at infinite volume.

Provided a method to recover interactions from correlation data.

Abstract

Given a classical gas described by the truncated correlation functions of all orders, we prove convergence of an expansion of the pair interaction part of the (unknown) potential in terms of the truncated correlation functions of all orders, at infinite volume.