  We study electron spin transport at spin-splitting surface of
chiral-crystalline-structured metals and Edelstein effect at the interface, by
using the Boltzmann transport equation beyond the relaxation time
approximation. We first define spin relaxation time and spin diffusion length
for two-dimensional systems with anisotropic spin--orbit coupling through the
spectrum of the integral kernel in the collision integral. We then explicitly
take account of the interface between the chiral metal and a nonmagnetic metal
with finite thickness. For this composite system, we derive analytical
expressions for efficiency of the charge current--spin current interconversion
as well as other coefficients found in the Edelstein effect. We also develop
the Onsager's reciprocity in the Edelstein effect along with experiments so
that it relates local input and output, which are respectively defined in the
regions separated by the interface. We finally provide a transfer matrix
corresponding to the Edelstein effect through the interface, with which we can
easily represent the Onsager's reciprocity as well as the charge--spin
conversion efficiencies we have obtained. We confirm the validity of the
Boltzmann transport equation in the present system starting from the Keldysh
formalism in the supplemental material. Our formulation also applies to the
Rashba model and other spin-splitting systems.
