Abstract
We investigate properties of the entropy density related to a generalized extensive statistics and derive the thermodynamic Bethe ansatz equation for a system of relativistic particles obeying such a statistics. We investigate the conformal limit of such a system. We also derive a generalized Y-system. The Gentile intermediate statistics and the statistics of gamma-ons are considered in detail. In particular, we observe that certain thermodynamic quantities for the Gentile statistics majorize those for the Haldane-Wu statistics. Specifically, for the effective central charges related to affine Toda models we obtain nontrivial inequalities in terms of dilogarithms.
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