Thermodynamic Bethe ansatz for generalized extensive statistics

TL;DR

This paper develops a thermodynamic Bethe ansatz framework for systems with generalized extensive statistics, analyzing their entropy, conformal limits, and deriving new Y-systems, with detailed studies on Gentile and gamma-on statistics.

Contribution

It introduces a generalized thermodynamic Bethe ansatz and Y-system for systems obeying extensive statistics, extending previous models and deriving new inequalities for effective central charges.

Findings

Certain thermodynamic quantities for Gentile statistics majorize those for Haldane-Wu statistics.

Derived nontrivial inequalities for effective central charges in affine Toda models.

Established a generalized Y-system for systems with extensive statistics.

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.