Equations of state in generalized hydrodynamics

TL;DR

This paper provides the first rigorous proof of the equations of state in generalized hydrodynamics for integrable systems, using a combinatorial graph-theoretic approach to Thermodynamic Bethe ansatz, demonstrating its universality.

Contribution

It introduces a first-principles, combinatorial proof of the equations of state in GHD, applicable to a broad class of integrable models.

Findings

Proof applies to relativistic integrable quantum field theories without bound states.

The graph-theoretic approach is universal across Bethe solvable models.

The method simplifies understanding of thermodynamic properties in integrable systems.

Abstract

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.