36 research outputs found
On completeness of description of an equilibrium canonical ensemble by reduced s-particle distribution function
In this article it is shown that in a classical equilibrium canonical
ensemble of molecules with -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 and a volume are fixed the
reduced -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 power series relative to the reduced
-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 don't possess such property and, to all appearance,
contain not all information about the system under consideration.Comment: This work was reported on the International conference on statistical
physics "SigmaPhi2008", Crete, Greece, 14-19 July 200
Best approximation by downward sets with applications
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x E X and W is a closed downward subset of X.C