I thank the authors for their in general adequate response and for the
amendments of their manuscript.
I made a few observations.
1) In the new final paragraph of section 1 the following sentence needs
"That is, we suppose that, at large times, the relevent of degrees of freedom
is reduced to the local mean charge densities..."
2) Thank you for extending appendix for explanations on "gauge covariance".
(In appendix C the word "gauge" is mispelled as "gaude".)
It is good to know that (top of page 11):
"It is possible to show, assuming the validity of the hydrodynamic projection
[72, 101], that the Onsager coefficients Lij are invariant under (2.28)."
"The hydrodynamic approximation of the currents (2.9) is explicitly dependent
on the choice of densities. See Appendix C."
but why do you say
"One must therefore choose a gauge in order to fix the diffusion matrix
Why not "Use any gauge and stick to it"? Maybe only very special gauges allow
for a hydrodynamical approach?
3) I am still having problems with appendix B. I find (B.3) problematic. The
derivation uses a generating functional with time-independent fields
\beta_j(x). Hence on the RHS of (B.3) instead of a two-point correlator with
second time variable identical to 0 an integral over a two-point correlator
with the second time variable as variable of integration should appear.
If (B.3) in the literal form is to be derived, the generating functional
should involve fields like \beta_j(x,tau).