On the completeness of describing an equilibrium canonical ensemble   using a pair distribution function
  It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle number $N$, volume $V$, and temperature $T$, the pair distribution function contains as many information about the system as a full Gibbs distribution. The latter is represented as a series expansion in the pair distribution function. A recurrence relation system is constructed, which allows all terms of this expansion to be calculated successively. 
M. I. Kalinin