A note on generalized hydrodynamics: inhomogeneous fields and other concepts

TL;DR

This paper extends generalized hydrodynamics (GHD) to include inhomogeneous external fields and all commuting flows, enabling better modeling of non-equilibrium dynamics in integrable systems like trapped Bose gases.

Contribution

It develops a comprehensive framework for GHD that incorporates weakly varying force and temperature fields, and derives equations of state from entropy continuity, advancing the theoretical understanding of inhomogeneous integrable systems.

Findings

Extended GHD to all commuting flows.

Derived equations of state from entropy continuity.

Discussed Euler-like equations and viscosity terms.

Abstract

Generalized hydrodynamics (GHD) was proposed recently as a formulation of hydrodynamics for integrable systems, taking into account infinitely-many conservation laws. In this note we further develop the theory in various directions. By extending GHD to all commuting flows of the integrable model, we provide a full description of how to take into account weakly varying force fields, temperature fields and other inhomogeneous external fields within GHD. We expect this can be used, for instance, to characterize the non-equilibrium dynamics of one-dimensional Bose gases in trap potentials. We further show how the equations of state at the core of GHD follow from the continuity relation for entropy, and we show how to recover Euler-like equations and discuss possible viscosity terms.