Haldane-Wu statistics and Rogers dilogarithm
Abstract
The Haldane-Wu exclusion statistics is considered from the generalized extensive statistics point of view and certain related mathematical aspects are investigated. A series representation for the corresponding generating function is proven. Equivalence of two formulae for the central charge, derived for the Haldane-Wu statistics via the thermodynamic Bethe ansatz, is established. As a corollary, a series representation with a free parameter for the Rogers dilogarithm is found. It is shown that the generating function, the entropy, and the central charge for the Gentile statistics majorize those for the Haldane-Wu statistics (under appropriate choice of parameters). From this, some dilogarithm inequality is derived.
Cite
@article{arxiv.math-ph/0211026,
title = {Haldane-Wu statistics and Rogers dilogarithm},
author = {Andrei G. Bytsko},
journal= {arXiv preprint arXiv:math-ph/0211026},
year = {2011}
}
Comments
9 pages, LaTeX2e, references added