Eur. Phys. J. C (2008) 58: 83-110
https://doi.org/10.1140/epjc/s10052-008-0724-1

Regular Article - Theoretical Physics

Multiplicity distributions in canonical and microcanonical statistical ensembles

¹ Helmholtz Research School, University of Frankfurt, Frankfurt, Germany
² University of Cape Town, Cape Town, South Africa
³ Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
⁴ Frankfurt Institute for Advanced Studies, Frankfurt, Germany

^* e-mail: hauer@fias.uni-frankfurt.de

Received: 16 November 2007
Revised: 28 July 2008
Published online: 23 September 2008

Abstract

The aim of this paper is to introduce a new technique for the calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. A Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace’s asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. A Gram–Charlier expansion additionally allows for the calculation of finite volume corrections. Analytical formulas are presented for the inclusion of resonance decay and finite acceptance effects directly into the partition function of the system. This paper consolidates and extends previously published results of the current investigation into the properties of statistical ensembles.