On the completeness of description of an equilibrium canonical ensemble using a reduceds-particle distribution function

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In this paper it is shown that for a classical equilibrium canonical ensemble of molecules with sufficientlysmall s-body interaction, the full Gibbs distribution can be uniquely expressed in terms of a reduceds-particle distribution function. This means that whenever the number of particlesN and the volumeV of such a system arefixed, the reduced s-particle distribution function contains as much information about theequilibrium system as the canonical Gibbs distribution function. The latter isrepresented as an absolutely convergent power series relative to the reduceds-particle distribution function. As an example, a linear term of this expansion iscalculated. It is also shown that reduced distribution functions of order less thans do not possess such a property and, to all appearances, do not contain all of theinformation about the system under consideration.