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FIZIKA A 14 (2005) 2, 119 - 134
 
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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