Completeness of the Description of an Equilibrium Canonical Ensemble by a Two-Particle Partition Function

We show that in the equilibrium classical canonical ensemble of particles with pair interaction, the full Gibbs partition function can be uniquely expressed in terms of the two-particle partition function. This implies that for a fixed number $N$ of particles in the equilibrium system and a fixed volume $V$ and temperature $T$, the two-particle partition function fully describes the Gibbs partition as well as the $N$-particle system in question. The Gibbs partition can be represented as a power series in the two-particle partition function. As an example, we give the linear term of this expansion.