FIZIKA A 14 (2005)  2, 119 - 134

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NEW DERIVATION OF THE CLUSTER CUMULANT FORMULA

D. K. SUNKO

Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32 HR-10 000 Zagreb, Croatia
E-mail address: dks@phy.hr

Received 14 December 2004;     Accepted 21 March 2005
Online 18 November 2005

The cluster cumulant formula of Kubo is derived by appealing only to elementary properties of subsets and binomial coefficients. It is shown to be a binomial transform of the grand potential. Extensivity is proven without introducing cumulants. A combinatorial inversion is used to reformulate the expansion in the activity to one in occupation probabilities, which explicitly control the convergence. The classical virial expansion is recovered to third order as an example.

PACS numbers: 02.70.Ns, 05.70.Ce, 31.15.-p
UDC 531.19

Keywords: Kubo formula, cluster cumulant expansion, virial expansion

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