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Completeness of the Description of an Equilibrium Canonical Ensemble by a Two-Particle Partition Function

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Abstract

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.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 123–132, October, 2005.

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Kalinin, M.I. Completeness of the Description of an Equilibrium Canonical Ensemble by a Two-Particle Partition Function. Theor Math Phys 145, 1474–1482 (2005). https://doi.org/10.1007/s11232-005-0173-z

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Keywords

  • equilibrium canonical ensemble
  • Gibbs partition
  • two-particle partition function
  • nonlinear operator equation
  • unique solvability