Haldane–Wu Statistic and Rogers Dilogarithm

The Haldane–Wu exclusion statistic 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 obtained. Equivalence of two formulas for the central charge derived for the Haldane–Wu statistic 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, entropy, and central charge for the Gentile statistic majorize those for the Haldane–Wu statistic (under an appropriate choice of parameters). This fact is applied in derivation of a dilogarithm inequality. Bibliography: 14 titles.