Title: On the completeness of description of an equilibrium canonical ensemble using a reduced<i>s</i>-particle distribution function
Abstract:In this paper it is shown that for a classical equilibrium canonical ensemble of molecules with sufficiently small s-body interaction, the full Gibbs distribution can be uniquely expressed in terms of...In this paper it is shown that for a classical equilibrium canonical ensemble of molecules with sufficiently small s-body interaction, the full Gibbs distribution can be uniquely expressed in terms of a reduced s-particle distribution function. This means that whenever the number of particles N and the volume V of such a system are fixed, the reduced s-particle distribution function contains as much information about the equilibrium system as the canonical Gibbs distribution function. The latter is represented as an absolutely convergent power 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 do not possess such a property and, to all appearances, do not contain all of the information about the system under consideration.Read More