Geodesic
Completeness of the Description of an Equilibrium Canonical Ensemble by a Two-Particle Partition Function
Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 1, pp. 123-132

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We show that in the equilibrium classical canonical ensemble of particles with pair interaction, the full Gibbs partition function can be uniquely expressed in terms of the two-particle partition function. This implies that for a fixed number $N$ of particles in the equilibrium system and a fixed volume $V$ and temperature $T$, the two-particle partition function fully describes the Gibbs partition as well as the $N$-particle system in question. The Gibbs partition can be represented as a power series in the two-particle partition function. As an example, we give the linear term of this expansion.
Mots-clés : equilibrium canonical ensemble, Gibbs partition
Keywords: two-particle partition function, nonlinear operator equation, unique solvability. 
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     title = {Completeness of the {Description} of an {Equilibrium} {Canonical} {Ensemble} by a {Two-Particle} {Partition} {Function}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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M. I. Kalinin. Completeness of the Description of an Equilibrium Canonical Ensemble by a Two-Particle Partition Function. Teoretičeskaâ i matematičeskaâ fizika, Tome 145 (2005) no. 1, pp. 123-132. http://geodesic.mathdoc.fr/item/TMF_2005_145_1_a6/