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Generalization of quantum statistics in statistical mechanics

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Abstract

We propose a generalization of quantum statistics in the framework of statistical mechanics. We derive a general formula which involves a wide class of equilibrium quantum statistical distributions, including the Bose and Fermi distributions. We suggest a way of evaluating the statistical distributions with the help of many-particle partition functions and apply it to studying some interesting distributions. A question on the statistical distribution for anyons is discussed, and the term following the Boltzmann one in the expansion of this distribution in powers of the Boltzmann factor, exp[β(μ-ɛi)], is estimated. An ansatz is proposed for evaluating the statistical distribution forquons (particles whose creation and annihilation operators satisfy theq-commutation relations). We also treat non-equilibrium statistical mechanics, obtaining unified expressions for the entropy of a nonequilibrium quantum gas and for a collision integral which are valid for a wide class of statistics.

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Authors and Affiliations

  1. Iinstitute of Medical Radiology, Obninsk, Kaluga Region, Russia

    S. B. Isakov

  2. Center “Sophus Lie”, Moscow, Russia

    S. B. Isakov

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  1. S. B. Isakov
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Isakov, S.B. Generalization of quantum statistics in statistical mechanics. Int J Theor Phys 32, 737–767 (1993). https://doi.org/10.1007/BF00671663

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