New derivation of the cluster cumulant formula
Statistical Mechanics
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0005018,
title = {New derivation of the cluster cumulant formula},
author = {D. K. Sunko},
journal= {arXiv preprint arXiv:cond-mat/0005018},
year = {2007}
}
Comments
pedagogically minded, minor changes as suggested by the referee, appeared in a memorial issue of Fizika A (Zagreb)