Equations of state in generalized hydrodynamics

We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound states such as strings.
Comment: 20 pages, 3 figures, v2 added reference v3 Submission to Scipost, TBA in abstract specified, remark on the originality of the proof added, the role of elementary form factors explained, T2 model presented in detail, similarity with classical hard-rod gases explained