On the completeness of description of an equilibrium canonical ensemble using a reduceds-particle distribution function
Journal of Statistical Mechanics: Theory and Experiment
In this article it is shown that in a classical equilibrium canonical ensemble of molecules with s-body interaction full Gibbs distribution can be uniquely expressed in terms of a reduced s-particle distribution function. This means that whenever a number of particles N and a volume V are fixed the reduced s-particle distribution function contains as much information about the equilibrium system as the whole canonical Gibbs distribution. The latter is represented as an absolutely convergent
... r series relative to the reduced s-particle distribution function. As an example a linear term of this expansion is calculated. It is also shown that reduced distribution functions of order less than s don't possess such property and, to all appearance, contain not all information about the system under consideration.