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Dimensionally regularized Boltzmann–Gibbs statistical mechanics and two-body Newton’s gravitation

Author

Listed:
  • Zamora, D.J.
  • Rocca, M.C.
  • Plastino, A.
  • Ferri, G.L.

Abstract

It is believed that the canonical gravitational partition function Z associated to the classical Boltzmann–Gibbs (BG) distribution e−βHZ cannot be constructed because the integral needed for building up Z includes an exponential and thus diverges at the origin. We show here that, by recourse to (1) the analytical extension treatment obtained for the first time ever, by Gradshteyn and Rizhik, via an appropriate formula for such case and (2) the dimensional regularization approach of Bollini and Giambiagi’s (DR), one can indeed obtain finite gravitational results employing the BG distribution. The BG treatment is considerably more involved than its Tsallis counterpart. The latter needs only dimensional regularization, the former requires, in addition, analytical extension.

Suggested Citation

  • Zamora, D.J. & Rocca, M.C. & Plastino, A. & Ferri, G.L., 2018. "Dimensionally regularized Boltzmann–Gibbs statistical mechanics and two-body Newton’s gravitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 793-799.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:793-799
    DOI: 10.1016/j.physa.2018.03.019
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    Cited by:

    1. Zamora, D.J. & Rocca, M.C. & Plastino, Angel, 2020. "Statistical Mechanics of planar stellar systems: Solving divergences in self-gravitational systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).

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