A note on generalized hydrodynamics: inhomogeneous fields and other concepts

Benjamin Doyon, Takato Yoshimura

Published 2016-11-24Version 1

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 also show that the GGE equations of state, and thus GHD, emerge uniformly in free particle models under the condition that the space-time variation scale of hydrodynamic observables grows unboundedly with time. 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.