Thermodynamic Bethe ansatz for generalized extensive statistics

We investigate properties of the entropy density related to a generalized e xtensive statistics and derive the thermodynamic Bethe ansatz equation for a system of relativistic particles obeying such a statistics. We investigat e the conformal limit of such a system. We also derive a generalized Y-syst em. The Gentile intermediate statistics and the statistics of gamma -ons ar e considered in detail. In particular, we observe that certain thermodynami c quantities for the Gentile statistics majorize those for the Haldane-Wu s tatistics. Specifically, for the effective central charges related to affin e Toda models we obtain nontrivial inequalities in terms of dilogarithms. ( C) 2001 Published by Elsevier Science B.V.