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Analytic representation of the equation of state in classical statistical mechanics

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Abstract

For a system of classical particles with short-range pairwise interactions, analytic representations of the spherically-symmetrical (uniform) compression modulus are constructed in terms of convergent series in the usual and complementary densities and in terms of contour integrals. Similar representations are given for the equation of state and the specific logarithm of the configuration integral. The uniform compression modulus, which appears to be single-valued in a vicinity of the phase transition, suffices to determine all of the interesting thermodynamic quantities. The techniques which we develop are tested by application to an exactly solvable model, the “Van der Waals substance,” which is a model “substance” whose exact equation of state is given by the Van der Waals equation.

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Authors and Affiliations

  1. P. N. Lebedev Center of Physical Investigations. P. N. Lebedev Physical Institute, Russian Academy of Sciences, USSR

    I. I. Ivanchik

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  1. I. I. Ivanchik
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 1, pp. 135–158, July, 1996.

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Ivanchik, I.I. Analytic representation of the equation of state in classical statistical mechanics. Theor Math Phys 108, 958–976 (1996). https://doi.org/10.1007/BF02070522

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