  We outline a general formalism of hydrodynamics for quantum systems with
multiple particle species which undergo completely elastic scattering. In the
thermodynamic limit, the complete kinematic data of the problem consists of the
particle content, the dispersion relations, and a universal dressing
transformation which accounts for interparticle interactions. We consider
quantum integrable models and we focus on the one-dimensional fermionic Hubbard
model. By linearizing hydrodynamic equations, we provide exact closed-form
expressions for Drude weights, generalized static charge susceptibilities and
charge-current correlators valid on hydrodynamic scale, represented as integral
kernels operating diagonally in the space of mode numbers of thermodynamic
excitations. We find that, on hydrodynamic scales, Drude weights manifestly
display Onsager reciprocal relations even for generic (i.e. non-canonical)
equilibrium states, and establish a generalized detailed balance condition for
a general quantum integrable model. We present the first exact analytic
expressions for the general Drude weights in the Hubbard model, and explain how
to reconcile different approaches for computing Drude weights from the previous
literature.
